Assiut University
Faculty of Engineering
Mining and Metallurgical Engineering Department
B. Sc. Project
Ore Reserve Estimation Using Computer Aided – A Case
Study of Mahamid Phosphate Mine
By
Baligh Hamdy et.al.
Supervisors
Prof. Dr.
Prof. Dr.
Dr.
Dr.
M. R. El-Tahlawi
M. Zaki Rashad
Gamal Y. Boghdady
SaMeH S. Ahmed
A dissertation submitted as part of the
B.Sc. Degree in Mining and Metallurgy Engineering
To Assiut University
July 2004
Abstract
Abstract
The Phosphate deposits in Egypt represent one of the most economic deposits with a
yearly production of …million tons. Those highly production are covered the local
market and about…..% of its …….. to several countries among there India,
and………….
The quality of the reserves is measured directly by its P2O5 %. The World wide
percentage should be above …..% P2O5 , The Egyptian phosphate has ….% in average.
This deposit are locality in the Eastern Desert at Kharga , Dakhla and Abu-Tartour
platue and distributed at the Eastern Desert at the Red Sea in Hamarwien , Qusier , and
around the Nile Valley at Sibaia and El Mahamid .
This study is focused in estimation of ore reserve at Eastern Mahamid district-using
computes facilitates, getting advantages of its fast accurate and easy way of calculation.
The principles of calculation are based upon the triangulation method where the
sampling area is divided into a triangulation net with known X, Y and measured of P2O5
of ore at each location.
Two ways have been implemented to conduct the calculations, the first is using Excel
software to determining the lengths of each triangle in the net from the coordinates, and
average thickness, and average assay of the ore, and thus estimate the average thickness
and assay of the ore in the study area. The same variables (average thickness of the ore
and average assay) have been determined using Kriging technique.
This study reviews the geological and geophysical aspects of the phosphate at the study
area and addresses the main mining method of ore extraction using surface mining.
Results of ore reserve estimation at Eastern Mahamid showed that the average thickness
of the ore deposit …and average P2O5.
340 sampling points taken from the area under study at El Mahamid district, Eastern
Desert of Egypt Were used to estimate the ore reserves of phosphate deposits and the
average thickness and average P2O5 content. The study has focused on applying an
approach supported with statistically steps that lead to an accurate and logic estimation.
The phosphate mining in Egypt represents one of the largest mining investments with
annual production of 56 million tons. These highly production are covered the local
market and about 80% of it exported to several countries, among them Ukraine and
India.
The quality of the phosphate ores is mainly determined by it percentage of P 2O5. The
accepted grade in the industry is 22%. Fortunately, the Egyptian phosphate has 25% in
average.
The use of computer facilities has become widely increased in different areas. Mining
engineering in general and ore reserve evaluation in particular are among these
applications. This project aims to determine the phosphate ore reserves at El Mahamid
area. Several factors have been taken into considerations during the calculations using
Excel software, such as providing robust, accurate, and easy use tool that would assist
the mining industry. The calculations have conducted based on the Triangular method,
statistical analysis of the raw sampling data. Giving X, Y, Z and one ore more variable,
for a certain area and with sufficient samples, the software has the capability of
determine the total area, volume, ore reserves, distribution of the variable under study
and point estimation for any un-sampled point within the entire area. The results are
i
Abstract
introduced as tables, figures, contour maps, and three-dimensional representation of the
variables.
On the other hand, the students have prepared a database for El Mahamied phosphate
mine to be added to the "Mining Information System (MIS..
ii
Acknowledgements
Acknowledgements
All gratitude is to God who guided and helped us to bring this work forward.
Sincere and heartfelt gratitude are expressed to the many individuals who have
helped to complete this work. Supervisory committee members gave us
generous portions of their time, their technical expertise, their support, and
their encouragements.
We would like to express our deep gratitude to Prof. M. R. El-Tahlawi,
Professor of Mining Geology in Mining Engineering Department, Assiut
University, for his sincere help, valuable advice, guidance and continual
assistance.
Grateful thanks are due to Prof. Mohamed Zaki Rashad, Professor of Mining
Engineering and Head of the Department, Assiut University, for his interest,
supports, and all efforts.
Grateful thanks are due to Dr. Gamal Yahia Boghdady, assistant Professor of
Structure Geology, Assiut University, for his help, and advice especially
through the mapping part.
We also desire to express our special and sincere gratitude to Dr. Sameh S.
Ahmad, assistant Professor of Mining and Environmental Engineering, Assiut
University, for his interest, effort, advice, and helpful remarks.
Our acknowledgment is extended to the people at the computer centre, library
and all workers in the department.
Finally, we would like to thank everyone who helped in one way or another in
making this work feasible.
The Students:
1. Ahmed Abdo Abbas
2. Ahmed Abdel Aleem Ahmed
3. Ahmed Abde Wahed Ahmed
4. Assma Abdel Azeem Mohamed
5. Ahmed Abdo Abbas
6. Ahmed Abdo Abbas
7. Ahmed Abdo Abbas
8. Ahmed Abdo Abbas
9. Ah Mahmoud Ali
11. Riad Gamal Riad
12. Maged Hanna Fangary
13. Mohammed Usama Ali
14. Samy Ebied Ewida
15. Riad Gamal Riad
16. Riad Gamal Riad
17. Riad Gamal Riad
18. Riad Gamal Riad
19.
iii
Table of Contents
Table of Contents
1.1
Introduction .......................................................................................................... 2
1.1.1 Classification of Phosphate Rocks ................................................................. 3
1.1.1.1 Classification according to its grade: ........................................................... 3
1.1.1.2 Classification according to its gangue minerals: .......................................... 3
1.1.2
Production Costs and Phosphate Availability .............................................. 3
1.2
Objectives .............................................................................................................. 4
1.3
Research Approach .............................................................................................. 5
1.4
Dissertation Organisation .................................................................................... 5
2.1
Introduction .......................................................................................................... 8
22
Geological Studies ................................................................................................ 9
221
Occurrence and origin of the world phosphate rock ................................... 9
2. 2. 2
Chemical and Physical Properties of Phosphate .................................... 11
2 .2 .2 .1 Colors ...................................................................................................... 11
2 .2 .2.2 Hardness ................................................................................................... 11
2. 2.3
Phosphate in Egypt .................................................................................. 11
2.2.4 Nile Valley Phosphate ................................................................................... 13
2.2.4.1 The Location and the topography .............................................................. 13
2.2.4.3 Geological setting....................................................................................... 13
2.2.4.4 The main features of the productive carbonate-phosphorite ...................... 14
2.3
Geophysical Investigation ............................................................................. 18
2.3.1 Importance of some logging methods ............................................................. 19
2.3.1.1 The GL method .......................................................................................... 19
2.3.2
Radioactivity logging .................................................................................... 20
2.3.3 Interpretation of gamma logging measurements ....................................... 20
2.3.3.1 Methods of interpretation ........................................................................... 21
2.3.4
Conclusions .................................................................................................... 21
3.1
Introduction ........................................................................................................ 24
3.2
Conventional Methods ....................................................................................... 24
3.2.1
3.3
Triangular Method ....................................................................................... 24
3.3.1
Geostatistics Techniques .................................................................................... 26
Variogram Modelling.................................................................................... 27
3.3.2 Kriging ........................................................................................................... 31
3.3.2.1 Equations for the Kriging system without and with a known mean ........... 32
3.3.2.2 Advantages of Kriging technique................................................................ 34
4.1
Introduction ........................................................................................................ 35
4.2
Summary Statistics for Area I............................................................................ 36
iv
Table of Contents
4.2.1
Summary Statistics for whole area .................................................................... 36
4.2.1.1
Summary Statistics for P2O5 .................................................................... 36
4.2.1.2
Summary Statistics for “t” ...................................................................... 38
4.2.2
Summary Statistics for Part I. a ........................................................................ 39
4.2.2.1
Summary Statistics for P2O5 .................................................................... 39
Percentiles for P2O5 ................................................................................................... 40
4 2 2 2 Summary Statistics for “t” ........................................................................... 41
Percentiles for “t” ...................................................................................................... 41
4.2.3
Summary Statistics for Part I. b ........................................................................ 43
4.2.3.1
Summary Statistics for P2O5 .................................................................... 43
Percentiles for P2O5 ................................................................................................... 43
4.2.3.2.Summary Statistics for “t” ................................................................................. 44
Percentiles for “t” ........................................................................................................... 45
4.2.4
Summary Statistics for Part I.c .......................................................................... 46
4.2.4.1 Summary Statistics for P2O5 .............................................................................. 46
Percentiles for P2O5 ........................................................................................................ 46
4 2.4 2 Summary Statistics for “t” ................................................................................. 48
Percentiles for “t” ........................................................................................................... 48
4.3
Summary Statistics for Area II .......................................................................... 49
4.3.1
Summary Statistics for whole area .................................................................... 49
4.3.1.1 Summary Statistics for P2O5 ........................................................................ 49
Percentiles for P2O5 ................................................................................................... 50
4.3.1.2. Summary Statistics for "t" ......................................................................... 51
Percentiles for “t” ...................................................................................................... 51
4.3.2
Summary Statistics for Part II.d ........................................................................ 53
4.3.2.1 Summary Statistics for P2O5 .............................................................................. 53
Percentiles for P2O5 ........................................................................................................ 53
4.3.2.2 Summary Statistics for “t” ................................................................................. 54
Percentiles for "t" ......................................................................................................... 55
4.3.3
Summary Statistics for Part II.e. ....................................................................... 56
4.3.3.1 Summary Statistics for P2O5 .............................................................................. 56
4.3.3.2 Summary Statistics for “t” ................................................................................. 58
Percentiles for "t" ......................................................................................................... 58
4.3.4
Summary Statistics for Part II.f......................................................................... 59
4.3.4.1 Summary Statistics for P2O5 .............................................................................. 59
v
Table of Contents
Percentiles for P2O5 ............................................................................................... 60
4.3.4.2 Summary Statistics for “t” ................................................................................. 61
Percentiles for t............................................................................................................... 61
4.3.5
Summary Statistics for Part II.g. ....................................................................... 63
4.3.5.1 Summary Statistics for P2O5 .............................................................................. 63
Percentiles for P2O5........................................................................................................ 63
4.3.5.2 Summary Statistics for “t” ................................................................................. 64
Percentiles for "t" ......................................................................................................... 65
4.3.6
Summary Statistics for Part II-h. ...................................................................... 66
4.3.6.1 Summary Statistics for P2O5 .............................................................................. 66
Percentiles for P2O5........................................................................................................ 66
4.3.6.2 Summary Statistics for “t” ................................................................................. 68
Percentiles for “t”........................................................................................................... 68
4.4
Summery of the Statistical Analysis and Discussion ........................................ 70
4.4.1
Analysis for the Overall Data ....................................................................... 70
4.4.2
Comments on the Results ............................................................................. 70
5.1
Introduction ........................................................................................................ 72
5.2
Original Sampling Data for Mahamied Phosphate Mine ................................ 73
5.3
Results of Triangular Method ........................................................................... 75
5.3.1
Upper Phosphate Seam ................................................................................. 76
5.3.2
Main Phosphate Seam .................................................................................. 82
5.4
5.4.1
Results of Ordinary Kriging Technique ............................................................ 83
Upper Phosphate Seam ................................................................................. 84
Main Phosphate Seam .............................................................................................. 86
5.5
Validation of the Results .................................................................................... 86
6.1
Introduction ........................................................................................................ 87
6.2
Surface Mining Method ..................................................................................... 88
6.2.1
General .......................................................................................................... 88
6.2.2
Advantages of surface mining ...................................................................... 88
6.2.3
Disadvantages ................................................................................................ 89
6.2.4
Factors favouring surface mining: .............................................................. 89
6.3
6.3.1
Surface or Underground Mining Methods? ..................................................... 89
6.4
Calculation of Stripping Ratio ..................................................................... 90
6.4.1
Height of bench .................................................................................................. 91
Height of bench due to stability of the face slope ....................................... 91
vi
Table of Contents
6.4.1.1
6.4.1.2
The Maximum height of the vertical face ............................................... 91
The limiting height of a vertical face ...................................................... 91
6.4.2 Height of bench due to safety of working place ............................................. 91
6.4.3
6.5
Height of bench calculated from the efficiency of work place .................. 91
Development schemes and mine trenches ......................................................... 92
6.5.1
Type of trenches ............................................................................................ 92
6.5.2
Shape of trenches: ......................................................................................... 93
6.6
Calculation of height of bench .......................................................................... 94
6.7
Drilling................................................................................................................ 95
6.7.1 Method of borehole drilling.......................................................................... 95
6.7.1.1 Rotary blast hole diameter: ..................................................................... 95
6.7.1.2 Percussive blast hole drilling for surface mining .................................... 96
6.8
Blasting ............................................................................................................... 97
6.8.1
Calculation of burden and spacing for 4 inch. borehole diameter: .......... 97
6.8.2
Calculation of burden and spacing for 2 inch borehole diameter: ........... 98
6.9
Loading and Unloading ..................................................................................... 99
6.10
Equipment ........................................................................................................ 100
6.10.1
Trucks ...................................................................................................... 100
6.10.2
Drag Line Specifications ......................................................................... 101
7.1
Conclusions ...................................................................................................... 104
7.2
Recommendations ............................................................................................ 105
W. M. Telford et al, 1974 "Applied Geophysics", Cambridge University. 860 P. ..... 108
I.1
X, Y Coordinates,"t"and P2O5 of Sampling Points at Mahamid ................... 109
II.1
X, Y Coordinates,"t" and P2O5 of Sampling Points ....................................... 112
III.1
Calculated tonnage and average assay at area II ........................................... 116
vii
List of Figures
List of Figures
FIGURE 1.1: A DIAGRAM EXPLAINS THE OBJECTIVES OF THE PROJECT ................................................... 7
FIGURE (2.1)
THE BELT OF THE PHOSPHATE ....................................................................................... 12
FIGURE 2.2
THE LOCATION MAP OF EL MAHAMID . ............................................................................. 17
FIGURE 2.3: A DIAGRAM OF GL & LCL. ................................................................................................... 19
FIGURE2.4................................................................................................................................................... 21
FIGURE 2.5. ................................................................................................................................................. 21
FIGURE 3.2: TRIANGULAR MODEL SHOWING DRILL HOLE LOCATIONS AT CORNERS OF TRIANGLES,
AND AVERAGE VALUE FOR THE HOLES. THE GRADE FOR EACH TRIANGULAR PRISM-SHAPED AREA
IS FOUND BY AVERAGING THE THREE VALUES AT THE CORNERS. ................................................... 25
FIGURE 3.3: VARIOGRAM PARAMETERS ................................................................................................ 28
FIGURE 3.4: COMMON VARIOGRAM MODELS, (AFTER, AHMED 2001) ................................................. 31
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART I) ................................................................................ 37
FIGURE 4.2.B:
HISTOGRAM FOR P2O5 (PART I) ..................................................................................... 37
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART I) .................................................................................. 38
FIGURE 4.2.B:
HISTOGRAM FOR “T” (PART I) ....................................................................................... 39
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART I. A) ............................................................................ 40
FIGURE 4.2.B:
HISTOGRAM FOR P2O5 (PART I. A) ................................................................................. 41
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART I. A) .............................................................................. 42
FIGURE 4.2.B:
HISTOGRAM FOR “T” (PART I. A) ................................................................................... 42
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART I.B) ............................................................................. 43
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART I.B) ................................................................................. 44
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART I.B) ............................................................................... 45
FIGURE 4.2.B:
HISTOGRAM FOR.”T” (PART I.B) .................................................................................... 46
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART I.C) ............................................................................. 47
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART I.C) ................................................................................. 47
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART I.C) ............................................................................... 48
FIGURE 4.2.B:
HISTOGRAM FOR.”T” (PART I.C) .................................................................................... 49
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART II) ............................................................................... 50
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART II) ................................................................................... 51
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART II) ................................................................................. 52
FIGURE 4.2.B:
HISTOGRAM FOR.”T” (PART II) ...................................................................................... 52
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART II.D) ........................................................................... 53
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART II.D) ................................................................................ 54
FIGURE 4.2.1:
QUANTILE PLOT FOR "T”(PART II.D) .............................................................................. 55
FIGURE 4.2.B:
HISTOGRAM FOR.”T”(PART II.D) .................................................................................... 56
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART II.E) ............................................................................ 57
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART II.E) ................................................................................ 57
FIGURE 4.2.1:
QUANTILE PLOT FOR “T”(PART II.E) ............................................................................... 58
FIGURE 4.2.B:
HISTOGRAM FOR. “T”(PART II.E) ................................................................................... 59
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART II.F) ............................................................................ 60
TABLE 4.1:
FREQUENCY TABULATION FOR P2O5 (PART II.F) ................................................................ 60
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART II.F)................................................................................. 61
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART II.F) .............................................................................. 62
TABLE 4.1:
FREQUENCY TABULATION FOR “T” (PART II.F) ................................................................... 62
FIGURE 4.2.B:
HISTOGRAM FOR. “T” (PART II.F) ................................................................................... 62
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART II.G) ........................................................................... 63
TABLE 4.1:
FREQUENCY TABULATION FOR P2O5 (PART II.G) ............................................................... 64
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART II.G) ................................................................................ 64
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART II.G) ............................................................................. 65
TABLE 4.1:
FREQUENCY TABULATION FOR “T” (PART II.G) .................................................................. 65
FIGURE 4.2.B:
HISTOGRAM FOR. “T” (PART II.G) .................................................................................. 66
FIGURE 4.2.1:
QUANTILE PLOT FOR P2O5 (PART II.H) ........................................................................... 67
viii
List of Figures
TABLE 4.1:
FREQUENCY TABULATION FOR P2O5 (PART II.H) ............................................................... 67
FIGURE 4.2.B:
HISTOGRAM FOR. P2O5 (PART II.H) ................................................................................ 67
FIGURE 4.2.1:
QUANTILE PLOT FOR “T” (PART II.H) ............................................................................. 68
TABLE 4.1:
FREQUENCY TABULATION FOR “T” (PART II.H) .................................................................. 69
FIGURE 4.2.B:
HISTOGRAM FOR. “T” (PART II.H) .................................................................................. 69
FIGURE 5.1: A CAPTURE FROM THE "O.R.E. SOFTWARE" SHOWING THE VALUES OF THE SAMPLING
POINTS (PART I) ................................................................................................................................ 75
FIGURE 5.2: A CAPTURE FROM O.R.E SOFTWARE SHOWING THE THICKNESS OF THE BOREHOLES (PART
I)
75
FIGURE 5.3:
CONTOUR MAPS FOR CARBON, ASH AND SULPHUR OF THE (PART I) USING THE
TRIANGULAR METHOD A) PLOTS USING SURFER 7 B) PLOTS USING O.R.E. SOFTWARE ................. 81
FIGURE 5.6: CONTOUR MAPS FOR CARBON, ASH AND SULPHUR OF THE (PART II), USING THE
TRIANGULAR METHOD A) PLOTS USING SURFER 7 B) PLOTS USING O.R.E. SOFTWARE ................. 82
FIGURE 5.7: OUTPUTS FROM VARIOWIN SHOWING THE VARIOGRAMS OF CARBON ........................... 83
FIGURE 5.8: CONTOUR MAPS AND 3D REPRESENTION FOR THE THICKNESS, ELEVATION AND
OVERBURDEN FOR (PART I), CALCULATED BASED ON (OK) ............................................................. 84
FIGURE 5.9: CONTOUR MAPS AND 3D REPRESENTATION FOR THE CARBON, ASH AND SULPHUR FOR
(PART I), CALCULATED BASED ON (OK) ............................................................................................. 85
FIGURE 6.1: SURFACE MINING PATTERN SHOWING EXTRACTION AND DEVELOPMENT (DIGISTAR,
2004). 88
FIGURE 6 2: MAIN OPERATIONS IN SURFACE AND UNDERGROUND MINING METHODS (DIGISTAR,
2004) 89
FIGURE 6 3: EXTRACTION OF ORE USING SURFACE MINING, (TAKEN FROM ELNASRMINING.COM). ... 90
FIGURE 6.4: TYPE OF TRENCHES, (AFTER, EL-ABDE RASSOUL, 1978). .................................................... 93
FIGURE 6.5: SHAPE OF TRENCHES. ......................................................................................................... 93
FIGURE 6.6: A PICTURE SHOWING THE BENCHES AND TRENCHES. (REFERENCE) ................................. 94
FIGURE 6.7: PERCUSSIVE DRILLS FOR REMOVING THE ORE AT EL MAHAMID. ...................................... 96
FIGURE 6.8: DRILLING OPERATION AT THE STUDY AREA (ELNASRMINING). ......................................... 97
FIGURE 6.9: REMOVING ORE (AFTER RANDALL, 1998). ......................................................................... 99
FIGURE 6.10:
LOADING OF PHOSPHATE AT THE EXTRACTION AREA OF MAHAMIED, PICTURE TAKEN
IN 2004. 100
FIGURE 6.11:
AN EXAMPLE OF THE TRUCKS USED AT EL MAHAMID. ............................................... 101
FIGURE 6.12:
DUMPING OF THE OVERBURDEN AT EL MAHAMID PHOSPHATE MINE. ..................... 101
FIGURE 6.1: A DIAGRAM FOR THE PROPOSED MINING INFORMATION SYSTEM (MIS) ....................... 103
FIGURE III.1:
TRIANGULATION NET OF ZONE "D" AT EL MAHAMID AREA II. ................................... 117
FIGURE III.2:
TRIANGULATION NET OF ZONE "E" AT EL MAHAMID AREA II. .................................... 117
FIGURE III.4:
TRIANGULATION NET OF ZONE "G" AT EL MAHAMID AREA II. ................................... 118
FIGURE III.5:
TRIANGULATION NET OF ZONE "H" AT EL MAHAMID AREA II. ................................... 119
ix
List of Tables
List of Tables
TABLE I-1: CONT. ...................................................................................................................................... 110
TABLE I.1: CONT. ...................................................................................................................................... 111
x
List of Abbreviations
List of Abbreviations
AR
Apparent Electric Resistivity.
GL
Gamma Logging.
SP
Potentials of Self-Polarization.
ML
Micro Logging.
LCL
Lateral Current Logging.
IMP/min
Impulses/min.
Cr2Vs
The Variegated Shales sub-Formation.
Cr2Ph
The Phosphorite sub-Formation.
Cr2Ph1
The Lower Productive Carbonate-Phosphate Member.
vod
Velocity of Detonation.
ANFO
Ammonium Nitrate and Fuel Oil.
OK
Ordinary Kriging
SD
Standard Deviation
SK
Simple Kriging
xi
List of Ssymbols
List of Symboles
B
Max. Height of burden.
K
Const. depending on rock characteristics.
d
Borehole diameter.
P
Detonation pressure.
T
Ultimate tensile strength of rock.
S
Spacing between boreholes.
H
Length of borehole
ρ
Density of explosives.
γ
Volumetric weight of the material.
α
Slope angle of slip plane.
H
Vertical face height.
C
Force of cohesion.
Hv
Maximum height of the vertical face.
φ
Angle of repose.
Hdmax
Maximum digging of the excavation.
a
Width of the broken down of material formed.
β
Slope angle of the face.
k
Loosening factor of the face material.

Ratio of length of least resistance line of first raw of blast holes to
height.
 
Ratio of distance between rows of blast holes to length of line of
least resistance.
Rd
Digging radius.
RL
Loading radius.
Chapter 1
Chapter
1.1
Introduction and Objectives
1
Introduction and Objectives
Introduction
Phosphate mining in Egypt started on 1940 when the first Phosphate mine was
inaugurated in Safaga, Qusseir, and Hamrawein.
In 1988, the exploit reserves in Egypt were 3325 million ton, which presented
6.22 % from the phosphate in Arab world
Phosphorus is the eleventh most abundant element in the lithosphere. Owing to
its relative reactivity, it generally is associated with calcium (Ca), sodium (Na),
fluorine (F), chloride (Cl), metals such as iron (Fe), aluminium (Al), magnesium
(Mg), heavy metals, for example cadmium (Cd), radionucleids like uranium (U)
etc.
Phosphate ores can be used in many industrial fields such as:
2
Chapter 1
Introduction and Objectives
1. The manufacture of the elemental phosphorous.
2. Phosphoric acid and its salts.
3. For making Ferro-phosphorous.
4. Metallurgical industries.
5. Phosphate ores are used in few cases for uranium extraction.
6. Fertilizer industry.
7. Photography.
8. Cosmetics.
9. Ceramics.
10. Insecticides.
11. Medicine.
1.1.1
Classification of Phosphate Rocks
1.1.1.1 Classification according to its grade:

Poor grade P2O5 ranges from (15-22%).

Medium grade P2O5 ranges from (22-27%).

Rich grade P2O5 grater than (28-38%).
1.1.1.2 Classification according to its gangue minerals:

Siliceous Ores:
These contain Qz, Chalcedony and different forms of silica.

Clayey Ores:
These mainly contain clays and hydrous iron and aluminum silicates or
oxides as gangue materials.

Calcareous Ores:
These contain calcite and dolomite as the major impurities with small
amounts of silica.
1.1.2
Production Costs and Phosphate Availability
A number of analysis on production costs for different producing mines and
potential mines and deposits have been made. The most significant factors
altering the cost situation for recovery and processing of phosphate rock and
3
Chapter 1
Introduction and Objectives
thus the profitability would be; accessibility of the ore, degree of beneficiation
required, capital investment, operating costs and, availability and cost of other
resources.(Phosphorus & potassium,1998).
Some calculations shown in Figure (1.1) are important for the estimates of the
amount of commercially exploitable phosphate deposits. There, calculations
were made in 1985; nevertheless the analysis is still relevant.
Figure 1.1
1.2
Phosphate rock production cost (Website, 2004).
Objectives
The main objective of this graduation project is to use the previous mining
courses and recent knowledge to re-estimate the ore reserves at Mahamied
Phosphate Mine, Esna, Egypt. Evaluating the ore reserves has been done using
the triangular method the methodology using Excel it has been taken into
consideration several factors that might affect the accuracy of estimating the
reserves using the manual method, among these factors, the screening and
statistical analysis of the raw data before calculations.
4
Chapter 1
Introduction and Objectives
Another objective of this graduation project is to use the available data and
information from El Mahamid Mine to add a new record to a big database for
the Egyptian mines.
1.3
Research Approach
The Egyptian Geological Survey has provided the data used throughout this
work. These data are given in Appendix I at the end of this dissertation. About
193 sampling boreholes with there X, and Y coordinates as well as P2O5 at part I
and part II of study area.
The work in this research can be divided into three main steps, see Figure (1.2).
Understanding the data by running an intensive statistical analysis over the
given data, such as screening the data to show the mean, modem, median,
minimum, maximum, range, standard deviation, skew, histograms, normality,
…etc.
Determining the ore reserves, all thickness and average assay and use it to
determining the tonnage and then calculate the total ore reserves. The
calculation has been done using Excel and based on the triangular method.
Preparing the data, the thickness and P2O5 to Mining Information System using
Database for Egyptian Mines and use El Mahamid Phosphate mine as a new
record to be added to the database this will be a part of a big project for the
Egyptian mines in the near future.
1.4
Dissertation Organisation
The dissertation lies in seven Chapters and two appendices in addition to a
Compact Disc (CD) for the results and information. Chapter one gives an idea
about the selected mining area and its historical background and the objectives
of the work followed by the approach applied to achieve the objectives. Chapter
two presents a literature review of the geological and geophysical studies of El
5
Chapter 1
Introduction and Objectives
Mahamid area, its location, formations, and structural geology. Chapter three
introduces the concepts and principles of the methods and techniques that used
throughout this work, mainly the triangular method, variorums, and Kriging
techniques. Chapter four starts with over viewing the available data at the
study area and proceeds to the statistical analysis of all the variables. and ended
with the possible correct sampling data that used through out the project for ore
reserve estimation and calculating the average thickness and average assay of
phosphate ore at El Mahamid area Chapter five illustrates the results obtained
from implementing the different methods and techniques for ore reserve
estimation and contouring the different variables, analysis and discussion of the
results. Chapter six addresses the possible information and data can be
to feed
MIS that would involve in the future all the Egyptian mines also highlights the
parameters and mining method. Finally, Chapter seven has reserved for the
conclusions and recommendations.
The dissertation presents in 116 Pages, 89 Figures and 37 Tables. The students
have used 5 Softwares’ programs and several computer facilities (Internet,
scanners, printers, and editing facilities) at the computer laboratory, Mining
and Metallurgical Engineering Department, Faculty of Engineering, Assiut
University.
6
Chapter 1
Introduction and Objectives
Figure 1.1:
A diagram explains the objectives of the project
7
Chapter 2
Chapter
2.1
Geological and Geophysical Studies
2
Geological and Geophysical
Studies
Introduction
The aim of this chapter is to review the geological and geophysical studies
related to the extraction of the phosphate ores in general, and thus focus on the
case of El-Mahamied phosphate ores, Esna, Egypt in particular.
This Chapter is divided into two main parts, the first is the background about
the geological studies and the second will cover the appropriate geophysical
methods or techniques that are used for exploration of phosphate deposits.
8
Chapter 2
Geological and Geophysical Studies
22
Geological Studies
221
Occurrence and origin of the world phosphate rock
There are two main types of phosphate rock deposits, igneous and sedimentary,
which
have
widely
differing
mineralogical,
textural
and
chemical
characteristics.
Marine sedimentary phosphate beds, such as those of USA, are marine chemical
deposits in large enclosed basins. This type also yields the important North
African production.
Apatite deposits are concentration of Apatite in begmatites, veins, and
magmatic segregation’s of igneous rocks. They are little worked today except in
Russia and Sweden.
Over 30 countries are currently producing phosphate rock for use in domestic
markets and/or international trade. The world’s top 12 producing countries
account for nearly 95% of the world’s total phosphate production. The three
major producing countries, i.e. the Morocco, China and USA, currently produce
approximately two thirds of global phosphate production.
Of these three major producers, Moroccan reserves account for around 50% of
the world total. Morocco is also in the most advantageous situation as its
potential reserves and geological in situ resources have been estimated to be
approximately 60% of total world resources. The USA and China have between
them around 20% of global resources.
Current World phosphate rock production capacity is estimated at around 165195 million tons/year, or approximately 50 or more million tons /year P2O5.
High – grade phosphate rock is available from many sources, such as Togo,
Senegal, and Morocco. (Phosphorus & Potassium, 1998).
9
Chapter 2
Geological and Geophysical Studies
Table (2.1) shows the amount of phosphate rock reserves in the most important
countries in the world.
Table 2.1
% of total
(1996)
United States
China
Morocco
Russia
South Africa
Tunisia
Jordan
Iraq
Brazil
Peru
All other
Countries
Global phosphate reserves, (After USGS, 1996).
Production
%
Reserves
Million ton
34
16
16
6
2
5
4
3
14
4 - 10
2 - 25
46 – 53
3
9 - 22
1
2-3
1
1-3
1
Potential
Reserves
Million ton
7 - 13
2 – 10
63
7 - 10
3 - 22
1
1–3
3
1-2
-
Geological
Reserves
Million ton
25
9
50
9
3
1-2
1-2
2-3
1
1-2
Table (2.2) shows the production of phosphate in the Arab World. (B.Sc 1988)
Table 2.2:
No
Arab country
Phosphate in Arab World
Exploit reserves
1
Morocco
40000
%
75.5
2
3
4
5
6
7
8
9
10
Egypt
Spanish Sahara
Iraq
Jordan
K.S.A
Syria
Algeria
Palestine
Tunisia
3325
3000
1760
1062
912
800
642
630
885
6.22
0.66
3.3
2.0
1.7
1.6
1.2
1.2
1.6
From the above table it is noticed that Morocco has the largest reserve in the
Arab World.
10
Chapter 2
Geological and Geophysical Studies
2. 2. 2 Chemical and Physical Properties of Phosphate
According to Pettijohn rocks containing more than (19.5%) P2O5 (about 50%
Apatite) are defined as phosphorites; if they contain more than (7.8%) P2O5
(about 20%Apatite), they are described as phosphatic.
2 .2 .2 .1 Colors
Phosphate rock is an earthy substance varying from a hard rock to a
granular, loosely consolidated mass. Its color may be brown, gray, bluish
gray, white or dark gray.
2 .2 .2.2 Hardness
It varies in apparent hardness from (2-5).
The Mineralogical Composition Of Phosphate Ores is shown in Table (2. 3).
Table 2. 3:
.No
1
2
3
4
5
6
2. 2.3
Minerals
Dahllite
Cllophane
Fluor Apatite
Chlor Apatite
Hydroxy Apatite
Apatite
Mineralogical composition.
Mineralogical Composition
9CaO.3P2O5.CaCo3.H2O
9CaO.3P2O5.CaCo3.H2O + H2O
9CaO.3P2O5.CaF2
9CaO.3P2O5.CaCl2
9CaO.3P2O5.Ca(OH)2
9CaO.3P2O5.Ca
Phosphate in Egypt
Phosphate ores, the principal mineral product of Egypt, are widely distributed
in four main localities, namely, The Eastern Desert, Sinai, the Nile valley and
the Western desert. The old phosphate mines at Safaga, Qusseir and
Hamrawein where actually working since 1940.(B.Sc project 1988).
The most important group of localities lies in the Qusseir-Safaga phosphatemining region in the Eastern Desert along the Red-Sea coast. The chemical
compositions of these phosphorites are the Calcium and \ or Magnesium
carbonates and Silica.
11
Chapter 2
Geological and Geophysical Studies
The second group of localities includes those of Dakhla-Kharge region and Abu
Tartur plateau. In Kharga, the P2O5 content of the phosphorite beds varies
widely from less than 10% to a max. of 28% . In Dakhla, the P2O5 varies from
(13-30%).
The third group of localities lies in the Nile valley and includes the districts of
Sibaiya and Idfo. The composition of the phosphorites varies according to the
nature of its cementing material, e.g., the carbonate variety contains the
following minerals: phosphate mineral (52.0), calcite (38.3), dolomite (1.4),
quartz (4.2), clay (2.0), gypsum (1.2), limonite (1.0).
The fourth group of localities of phosphate rock, which comprises minor
deposits, occurs in the Gulf of Suez and central Sinai area. This includes Gabal
el-Zeit, in The Eastern Desert, as well as wadi Gharandal and Gabal Tanka on
the Eastern coast of the Gulf of Suez in Sinai. Figure (2.1) shows the belt of the
phosphate in Egypt:
Figure (2.1)
The belt of the phosphate
12
Chapter 2
2.2.4
Geological and Geophysical Studies
Nile Valley Phosphate
The Nile valley phosphorite deposit is a part of the vast upper cretaceous
marine phosphorite basin, which covered a considerable part of the Egyptian
territory, and extended father into Jordan, Palestine, Syria and Iraq. The thickest
accumulation of the Egyptian phosphoites occur along the base of the sequence
at Abu Tartur (Kharga Oaasis), near the top of the sequence in the base and top
of the sequence on the Red sea coast. These phosphorites are commonly
composed of multiple accumulations of thinner individual beds. The
phosphate-bearing sediments in the Nile valley region belong to the Duwi
formation and having a total thickness of 25-40 m.
2.2.4.1 The Location and the topography
El Mahamid deposit occupies a vast area of a bout 250 km2. Along the
left and right banks of the Nile, to the south of the Qena and Luxor,
between the towns of Esna and Idfu. The bounding coordinates latitudes
(250 15/and 250 5/ N) and longitudes (330 32/ and 330 00/ E) .the area of
the deposit is separated by the Nile Valley into the western Mahamid on
the left bank and the eastern Mahamid on the right bank.
2.2.4.2 Stratigraphy and position of the phosphorites in the succession
The Cenomanian stage

The Cenomanian-Santonian-Campanion stages

The Campanian stage

The Danian stage

The Paleocene

The Lower Eocene
2.2.4.3 Geological setting
El Mahamid deposit is mainly confined to the upper cretaceous marine
sediments distributed in both the eastern and western areas. The
overlying Paleocene sediments form the topographic highs, which limit
the eastern area from the north and North-West. Stratigraphically, the
13
Chapter 2
Geological and Geophysical Studies
upper cretaceous sediments are represented by rocks of the Campanian
and Maestrichtian stages and are subdivided into two formations, which
are, from bottom to top, the Duwi and Dakhla formations.
The Duwi formation (companion)
In the area of the deposit, this formation is litho logically subdivided into
two sub-formations namely:

The variegated shales sub-formation (Cr2 VS).

The phosphorite sub-formation (Cr2 Ph).

The important sub-formation is the second one (Cr2 Ph) it is measure
from (20 to 32 m) in thickness and is subdivided into three members:

Lower productive carbonate-phosphorite member (from 2-3 to 10-12 m).

Middle phosphorite-clayey member (from 6-12 m).

Upper phosphorite-clayey member (from 7-10 m).
The lower productive carbonate-phosphorite member (Cr2 Ph1), which
includes commercials phosphorite beds, is the main object of the
investigations carried out in the area.
2) The Dakhla formation (Maestrichtion)
The Dakhla clays, in general, do not contain neither phosphorite
intercalation nor poor phosphatic marls and limestone.
2.2.4.4 The main features of the productive carbonate-phosphorite
Phosphate El Mahamid included two features, are given below:

Western Mahamid.

Eastern Mahamid.
1) Eastern Mahamid
The productive member in the Eastern Mahamid area is rather variable.
Accordingly, the different prospected areas will be dealt with separately:

The Sharawna area.

The Oweiniya area.

The Hagariya and Qurayat areas.
14
Chapter 2

Geological and Geophysical Studies
Mussattah Yassin.
1) Sharawna area; in this area the productive member lies a relatively great
depth from the surface. The features of this area are:
Over the greater part of the area, the average p2o5 content (20-22%). And the
average thickness of the bed is (0.65-0.70 m).
The lower and upper phosphorite beds with thickness (1.0-1.2 m).
The upper phosphorite bed with an average content (18-19%P2O5), and poor
oyster phosphorites with (10-12%P2O5) and with thickness of (0.8-0.95 m).
2) The Oweiniya area, this area is the continuation of the Sharawna area, the
features of this area are:
The lower phosphorite bed attains an average thickness of (0.5-0.6 m). With
content of (8-15 % P2O5).
The carbonate- bearing ores, the average thickness of these carbonate rocks is
range from (3.0-3.5 m) sometimes it reaches 5 m.
Both the upper and lower phosphorite beds are characterized by facial nonpersistence.
A Poor phosphatic oyster limestone bed, up to 4.5 m thick.
3) The Hagariya and Qurayat areas, the features of these areas are;
The lower phosphorite bed with average content of (24-26 %P2O5) and its
average thickness is (0.6 m) at Hagariya and (0.8 m) at Qurayat.
The carbonate rocks are represented by poor phosphatic marls ranging in
thickness from (0.5-0.6 m) at Qurayat, and from (0.8-1.0 m) at Hagariya.
The upper phosphorite bed of the Hagariya area, its thickness ranges between
(0.2-1.5 m).
15
Chapter 2
Geological and Geophysical Studies
The section of the productive member is terminated by poor phosphatic marls
and oyster limestones.
4) Mussattah Yassin area, the features of this area are:
The lower phosphorite bed, with average content ranging between (17-18% and
23%). Its average thickness is (0.65-0.7m).
The poor phosphatic oyster limestones from abed (2.0 to 4.0m) thick.
The upper phosphorite bed, with average content of (16-19%p2o5). Its thickness
does not usually exceed (0.45 m).
The section of the productive member is terminated on top by a bed of poor
phosphatic oyster limestone. Figure (2.2) shows the location of El Mahamid
area;
16
Chapter 2
Geological and Geophysical Studies
El Mahamid
Figure 2.2
The location map of El Mahamid .
17
Chapter 2
2.3
Geological and Geophysical Studies
Geophysical Investigation
Geophysical methods have been applied to the investigation of drill holes for
some forty-five years. Using initially the same electrode techniques as in surface
exploration. The various instruments and techniques, specifically designed to
suit the different environment in drill holes, are used in direct exploration,
identification of geologic formation and formation fluids, and correlation
between holes.
Geophysical methods which have been applied in well logging include
resistivity, self-potential induction, induced-polarization and occasionally other
electrical methods, detection of gamma-rays and neutrons in radioactivity
methods, acoustic logging, and measurement of magnetic and thermal
properties. (Applied Geophysics 1974).
The aim of logging operations was to determine:

Thickness

Structure

Depth of occurrence of the phosphorite- bearing beds
The work was started in October 1966 and had been continued till the middle of
December 1967.During this time 228 bore hole were logged (in this number 118
in the area of western Mahamid, 110 in the eastern Mahamid) which amount to
about 65% of the total number of the drilled bore holes (The total amount of
bore holes are 350 In this study we work with 201 B.H. which presented 57 %
from the total number of the area) (Dr. Rushdi Said, 1968 ).
The following logging methods were tried:

AR (apparent electric resistivity)

GL (gamma logging)

SP (potentials of self-polarization)

ML (micro logging)
This work resulted in recognition of the preliminary characteristics of the
section by its physical properties:
18
Chapter 2
Geological and Geophysical Studies
Apparent electric resistivity
Natural gamma activity
Natural electro –chemical activity
The above work aimed to obtain:

Data concerning phosphorites

Summarize data on detect ability of each of the method

Study practical possibilities of these methods

The geological setting of the deposit
It was stated that the depth of the bore holes ranges from (8-35m) and logging
intervals vary from (4-25m)
2.3.1 Importance of some logging methods
2.3.1.1 The GL method
Allows to detect with assurance phosphate- bearing beds as no other
rocks with increased intensity of natural gamma – radiation occur in the
section.
Accuracy in definition of the bed structure will be increased if to
interpret simultaneously the diagrams of GL and LCL (Figure (2.3)).
1-Cable-.K.T.SH- 2
2-The body of GL Borehole apparatus, it
is also used as screen electrode A1,A2
OFL
3-Free wire of the cable
4-Rubber insulator
5-Lead electrode. A0
RE – Equivalent resistance of GL
apparatus scheme
Figure 2.3:
A diagram of GL & LCL.
2-The Lateral Current Logging (LCL) curves
19
Chapter 2
Geological and Geophysical Studies
a) Allows to distinguish in the phosphorite bed barren interbeds
b) Understand their contacts, so a joint use of the GL & LCL methods
enables to solve satisfactory the tasks of logging.
3-The method of AR
Electrochemical activity and ML were not used in a further work.
2.3.2
Radioactivity logging
Gamma Logging (GL): Gamma logging was used for detecting the phosphorite
beds and the other rock types.
2.3.3
Interpretation of gamma logging measurements
Different intensity levels of gamma radiation were recorded inside every bore
hole which corresponds to different concentration of radioactive elements in the
rocks, within the geological section measured, the a mount of radiation
characterized a certain type of rocks. Thus, depending on the concentration of
the radioactive elements.
There are many factors that may affect the intensity of gamma radiation; the
cementing materials; solidification of phosphorites; grain size; cavities; and
casing pipes in bore holes and mud fluids.
All the measurements of gamma logging are expressed only in imp/min
(impulses/minute).
It represents a cylindrical metallic capacity, hermetically sealed, with the hole in
the center of the axis. The diameter of the hole is equal to that of the welldevice. The capacity was completely filled with crushed phophorite.
Gamma logging diagrams were recorded in two scales:
1-1:100 searching and the speed of recording was 500-700 m/h
2-1:50 detailed one and the speed of recording not more than 300 m/h
20
Chapter 2
Geological and Geophysical Studies
2.3.3.1 Methods of interpretation
Experimental operation by the GL method was carried out at the model B.H.
aiming at checking the methods of interpretation applied. The diagrams
obtained were interpreted and compared with the real section of the model. In
all cases discrepancy in thickness did not exceed  5 cm. (see Figures (2.4), (2.5).
Figure2.4.
Figure 2.5.
2.3.4
Conclusions
As it was mentioned above in the area under investigations all the phosphorites
are characterized by the increased radioactivity and apparent resistivity. These
physical properties of the phosphorites are favorable for their detection in the
section with the help of;
21
Chapter 2
Geological and Geophysical Studies
Gamma logging (GL)
Lateral current logging (LCL)
The arithmetical mean error in determination of thickness by means of logging
was calculated to be (plus or minus 0.09 m or 11% from the 0.76 m).
A remarkable dependence was noted between the intensity of natural gamma
radiation and P2O5content in the productive beds. This served as the basis for
searching of quantitative characteristic of such dependence.
I (gamma) = f (P2O5%).
Where;
I (gamma)
is intensity of natural gamma activity according to the GL data.
P2O5
is content in percent by the chemical analysis data.
Efficiency of logging in prospecting of the phosphorite deposits can be
quantitatively estimated .The results of the control drilling and pitting showed
that the thickness of the phosphorite horizons, according to the logging data,
were determined with average increase equal to 20% over the whole area under
studies.
The cost of the logging team does not surpass 3% from the total expenses on
geological and prospecting works all this evidence indicates convincingly
geological and economical efficiency of logging all stages of prospecting for
phosphorites.
From the above work we can say that we use both of GL & LCL methods for the
investigation in El Mahamid area, the actual amount of bore holes used were
201B.H. In the next chapter we will illustrate the statically analysis of the data
and calculation of average thickness, average grade of P2O5 in the area with
22
Chapter 2
Geological and Geophysical Studies
different methods In addition to Wadies running off the scraps, there are other
more major ones running parallel to the strike or in faulted areas, and the access
road makes use of two such Wadies, the Masagid and the Muzeira. These larger
Wadies often have deep alluvium, sometimes with readily apparent terrace
levels, probably a result of the very different climatic conditions from late
Pliocene to early Pleistocene times.
23
List of Ssymbols
Chapter
3.1
3
Ore Reserve Estimation
Methods and Techniques
Introduction
The purpose of this Chapter is to demonstrate the principles, concepts and
mathematical functions for the methods and techniques that are using for ore
reserves estimation. It is proposed to examine two conventional methods
(Polygon method and Triangular Method) and one of the geostatistics
techniques (Ordinary Kriging).
3.2
Conventional Methods
3.2.1
Triangular Method
The triangular method is similar to the polygonal method. It calculates the
volume of a triangular-shaped prism formed between three adjacent drill holes
Chapter 3
Ore Reserve Estimation Methods and Techniques
(Figure 3.2). Like the polygonal method, bench levels are specified. Grade
determinations for the prisms are determined differently than the polygon
model. In the triangular model, the grade is determined by averaging the value
of the three values at the corners of each triangle.
3
2
1
5
4
8
7
6
Borehole Grade%
Triangle
1
2
3
4
5
6
7
8
1-2-4
1-4-6
2-3-5
2-4-5
3-5-8
4-5-7
4-6-7
5-7-8
0.12
0.21
0.17
0.50
0.33
0.05
0.26
0.15
Figure 3.2:
Average
Grade%
0.277
0.223
.0.237
0.346
0.217
0.363
0.270
0.247
Area
m²
14.5
21.6
21.1
26.2
14.9
28.2
29.7
22.3
Results
Total Area
= 178.5
Total Area * Grade=49.9
Average Grade
= 0.280
Triangular model showing drill hole locations at corners of triangles, and average value
for the holes. The grade for each triangular prism-shaped area is found by averaging the
three values at the corners.
A) For each triangle
1) Average thickness ( h Av. ) =
h1  h2  h3
…….…………………………(3.1)
3
2) Average assay ( AAv. )
=
A1h1  A2 h2  A3 h3
…………………...…..(3.2)
h1  h2  h3
3) Area (a)
=
p p  L1  p  L2  p  L3  …………..…..(3.3)
=
a1h1  a2 h2  a3 h3  ..........  an hn
……..….(3.4)
a1  a2  a3  ..........  an
B) For whole area
1) Average thickness
25
Chapter 3
Ore Reserve Estimation Methods and Techniques
2) Average assay
=
a1hAv.1 AAv.1  a2 hAv.2 AAv.2  a3 hAv.3 AAv.3  ..........  an hAv.n AAv.n
………....(3.5)
a1hAv.1  a2 hAv.2  a3 hAv.3  ..........  an hAv.n
3) Volume
  Area * Averagethickness ……………….(3.6)
4) Tonnage

Volume
.……………………………………(3.7)
T .F
Where:
3.3
h:
A:
a:
T.F:
Thickness of borehole, m
Assay of metal, %
Area of triangle, m2
Tonnage Factor, t/m3
L:
p:
Length of triangle side
Half periphery of triangle
=  X 1  X s   Y1  Ys 
= (L1+L2+L3 )/2
2
2
Geostatistics Techniques
Geostatistics is the statistics of spatially or temporally correlated data . The
technique has been used to be a practical approach to the problems of ore
reserve estimation and mine planning. It has been also used for other
applications concerned with petroleum and gas resources estimation.
One of the characteristics that distinguish earth sciences data from most other
data is that the data belongs to same location in space. Spatial features of the
data set such as the location of extreme values, the overall trend, or the degree
of continuity are of considerable interest (Isaaks and Srivastava, 1989). These
features, in other words the variables Z(x), are functions describing natural
phenomena that have geographic distributions, such as the elevation of terrain,
the depth of groundwater table, or the ore grade within an ore body.
In Practice, the application of geostatistics techniques is carried out in two
fundamental steps:
1. Construction of the variograms
2. Conducting one of the suitable Kriging technique
26
Chapter 3
3.3.1
Ore Reserve Estimation Methods and Techniques
Variogram Modelling
A variogram is graph illustrating the average variability between samples and
the distance between samples. The variogram can be described as variation in
values among samples some distance apart as a measure of their spatial
correlation.
The mathematical formulation of variogram function is as follow:
2
N
1
z( xi )  z( xi  h ) .……………………………………(3.8)
 (h) 

2 N ( h ) i 1
Where Z(Xi) and Z(Xi+h) are two samples at Xi and Xi+h locations separated by
h distance.
The simplest method of comparing two sample values is to calculate the
difference between two samples. When comparing a large number of sample
pairs, the following will be found.
Some difference will be positive and some will be negative. By squaring the
difference, all become positive.
Differences are measured between samples at similar distances apart are
squared and averaged.
One the results of these samples mean-squared difference measurements
difference measurements are calculated, they can be displayed as simple X-Y
scatter plot. Distance between samples is plotted on the X-axis and is labeled
with an h; and, average squared differences between samples are plotted on the
Y-axis and are labeled with the Greek letter for Gamma (γ). This graph is called
a variogram by geostatisticians. After the graph is constructed, a line is drawn
connecting the posted data. This variogram or semivariogram is commonly
referred to as the experimental variogram. (Rashad 2002)
Semivariogram is another term commonly used by geostatisticians.
27
Chapter 3
Ore Reserve Estimation Methods and Techniques
Semivariogram plot distance (h) verses one-half the average squared differences
(γ/2) rather than distance verses average squared differences as with the
variogram. Semivariograms use the one-half factor so that plotted values are
equivalent to the statistical variance. Most geostatistical practitioners calculate
semivariogram, but refer to the displayed results as variograms.
The shape of the variogram does not change when 2 divide the Gammas.
The final step in analyzing the variogram is to compare the experimental
variograms to models, which can be characterized by mathematical functions.
This comparison about statistical spatial data variability can be made.
The process of construction and modeling variogram is called variography.
Figure 3.3, shows the main parameters calculated from the variograms, which
Variogram (γ)
are defined in Table 3.1.
Figure 3.3:
Variogram parameters
28
Chapter 3
Ore Reserve Estimation Methods and Techniques
Table 3.1:
Nugget Effect
Definition of variogram parameters
Quantifies the sampling and assaying errors and the short scale
variability (i.e. spatial variation occurring at distance closer
than the sample spacing).
Scale (C)
Is the vertical scale for the structured component of the
variogram Each component of a variogram model has its own
scale.
Sill
Is the total vertical scale of the variogram (Nugget Effect + Sum
of all component scales) Linear, Logarithmic, and power
variogram models not have a sill.
Length
Is the horizontal range of the variogram (Some variogram
models do not have a length parameter; e.g. the linear model
has a slope instead).
Variance
Is the mean squared deviation of each value from the mean
value Variance is indicated by the dashed horizontal line in the
diagram shown above.
Pairs
Represents the average value for the group of pairs separated
by a specified distance (lag width) the number adjacent to the
square symbols indicates the number pairs within each lag
distance.
Model Curve
Shows the shape of the variogram model.
Experiment
Curve
Displays the groups of variogram pairs on a plot of separation
distance versus the estimated variogram.
In order to be able to define characteristic quantities for the semivariogram, a
model is often assumed. The basic variogram models, which are simple and
isotropic, can be divided into two types. Those that reach a plateau and those
29
Chapter 3
Ore Reserve Estimation Methods and Techniques
that does not. The most common variogram models are presented in Figure 3.4.
The models occurring most often in literature are the spherical, the exponential,
and the Gaussian (Isaaks and Srivastava, 1989).
Spherical model: is probably the most commonly transition model. It is
equation is given by:
C 0  C[3h / 2a  (h 3 / 2a 3 )]
ha
...........
…………………………….(3.9)
ha
C 0  C
 ( h)  
Where:
C0
C
C0 + C
a
is the random component of variation, i.e. the nugget effect variance.
is the structural component of the variance.
is the total variation or sill.
is the range of influence.
Exponential model: is another commonly used transition model. Its equation is
given by:
 (h)  C0  C[1  exp( 3h / a)] ………………...……………………………….(3.10)
Gaussian model: is a transition model that is often used to model extremely
continuous phenomena. Its equations is:
 (h)  C 0  C[1  exp( 3h 2 / a 2 )] …………………………………………..….(3.11)
Power model: linear model is not a transition model since it does not reach a
sill, but increases linearly with h. In its standardised form it is written simply
as:
 (h)  C 0  C h …………………………………………………………...….(3.12)
a
Where:
a
is the slop.
A variogram model should not be needlessly complex. Ideally, each variogram
structure should have a physical interpretation. The more complicated the
variogram model, the longer it takes to construct each Kriging matrix; hence,
the longer the Kriging or simulation program will take.
30
Chapter 3
Ore Reserve Estimation Methods and Techniques
h)
h)
Sill
C
C0
range
a
h
Spherical model
Exponential model
h)
h)
h
h
Linear model
Figure 3.4:
3.3.2
h
Gaussian model
Common variogram models, (after, Ahmed 2001)
Kriging
The Kriging technique is named after the South African geostatistician D. J.
Krig. It is a technique for determining the best linear unbiased estimator with
minimal estimation variance. It can be used on a point as well as on a block A
Block is simulated by numerous point that are then integrated (Wellmer, 1998).
Kriging was developed for the very specific application of predicting gold
reserves in mines in South Africa from borehole information. It owes a great
deal to the contribution of Matheron and his co-workers at the Ecoles des Mines
(Mackay and O’Connell, 1991).
Swan and Sandilands (1995) studied the difference between Kriging techniques
and the other estimation methods and found that Kriging is a different and
spatial way of making estimates of spatially distributed values from point
value. The following are the key elements involved:
Several Kriging techniques have found in literature. According to different
requirements of different problems, one refers to simple Kriging when the
mean is known and constant; universal Kriging and intrinsic Kriging that allow
31
Chapter 3
Ore Reserve Estimation Methods and Techniques
fluctuations in the mean; log-normal Kriging when processing the logarithms of
the original data; or other types of Kriging techniques described in literature.
The following section describes the equations of the Kriging system.
3.3.2.1 Equations for the Kriging system without and with a known mean
The Kriging matrix K contains the variance (e.g.σ11) and covariance (e.g.σ12) of
all the points Xi (I=1, 2, ……, n) around the reference point P that are included
the weighted σij is the covariance between the values Xi and Xj, or (Xi ,Xj)
Cov(Xi, Xj), σii are the covariance’s of a point with respect to itself (where h =
0),and thuth are identical with the variance.
 11

 21

K 

 n1
 1

 12 ...........................  1n
 22 ...........................  2 n
:
:
 n 2 ...........................  nn
1
1
1
1 

 ……………………………...….(3.13)

1
0
This is the Kriging matrix for case (a) (Kriging without a mean).The final row
and column are missing from the matrix for case (b) (Kriging with known
mean)
Since
σik = σki
the matrix is symmetrical and, for example, σ12 = σ21 regardless
of whether point 1 is viewed from point 2 or the other way round, the
covariance between point 1 and 2 must be the same. The spacing between the
two points is the same, and it is this dimension that determined the covariance,
which can be derived from the variogram.
The weighting factors λi describe a vector, λ . In addition, the LaGrange
multiplier μ is introduced for the case (a) of Kriging without a mean. This
parameter does not occur in case (b) (Kriging with a known mean).
32
Chapter 3
Ore Reserve Estimation Methods and Techniques
 1 
 
  2 
  :  …………………………...….…………………………...….………...….(3.14)
 
 n 
 
The third dimension in Eq. (3.16) see below is the vector D . This vector contains
the covariance’s of the reference point P to all the other points that are being
taken into consideration:
 p ,1 


  p , 2 
D  :
 …………………...….…………………………...….………...….(3.15)
 
 p ,n 
 1 
This is also the vector for the case (a) (Kriging with an unknown mean). The
final value 1 dose not occurs in case (b) (Kriging with a known mean).
The following relationship between the Kriging matrix and the two vectors is
then true:

k    D ...….………...….………...….………...….………...….………..(3.
16)
Consider, for example, the reference point P and two additional points 1 and 2,
then the system (3. 16) above for case (a) (Kriging without a mean) is:
 11  12

 21  22
 1
1
1  1   p ,1 
1  2    p , 2  ……...….………...….………...….……….……...(3.17)
0     1 
For case (b) (kriging with a known mean), the system (3.16) above, for the
reference point P and two additional points1 and 2 is:
 11  12   1   p ,1 
 …...….………...….………...….……….……...............(3.18)

   
 21  22  2   p , 2 
33
Chapter 3
Ore Reserve Estimation Methods and Techniques
The computation of this matrix system is as follows: each value in a row of the
matrix is multiplied by the corresponding value for the vector, and then they
(row X column) are summed together.
In case (a) (Kriging without a mean) this yield the following system of
equations:
 11  1   12   2     p ,1 ...….………...….…….….……….……..................(3.19)
 21  1   22   2     p , 2 ………...….………..….……….……...............….(3.20)
1  1  1  2  o    1……............………………………….……………...….(3.21)
This is system of three equations with the three unknowns 1 ,  2 and  . In case
(b) (Kriging with a known mean), the system is as follows:
 11  1   12   2   p ,1
 21  1   22   2   p , 2
…………………………….……………………....….(3.22)
The unknown μ is missing from this system, and therefore it is a simpler system
with only two equations.
3.3.2.2 Advantages of Kriging technique
The technique has the following useful attributes:
1. it is an exact interpolator, it returns the observed values at measurement
points.
2. it is a best linear unbiased estimator.
3. the Kriging equations do not involve the measured values.
4. measurements which represent averages over some specified area
5. measurement errors can be accounted for (Mackay and O’Connell, 1991).
34
Sampling Data and Statistical Analysis
Chapter
4.1
4
Sampling Data and Statistical
Analysis
Introduction
The data used throughout this research are collected from 19 boreholes at the
(PART I) and 29 boreholes at the (PART II) of Mahamied Phosphate Mine. For
each sampling borehole X, Y, Z, thickness of overburden, and thickness of the
seam were measured. Most of the borehole samples have a complete analysis
for the following one main variable: P2O5.
The aim of this Chapter is to screen the data and test the main statistical
parameters, such as, measure of location, measure of shape and measure of
spread. Each set of variables has been tested separately and a summary of the
overall data is given at this end of the Chapter.
Chapter 4
Sampling Data and Preliminary Statistical Analysis
A complete record of the raw data for both (PART I) and (PART II) is given in
Appendix I including the chemical analysis of the sampling boreholes.
4.2
Summary Statistics for Area I
4.2.1 Summary Statistics for whole area
4.2.1.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 70
= 23.1889
= 21.1595
= 4.59995
= 8.19
= 29.84
= -4.05057
= 2.54084
This table shows summary statistics for P2O5. It includes measures of central tendency,
measures of variability, and measures of shape. Of particular interest here are the
standardized skewness and standardized kurtosis, which can be used to determine
whether the sample comes from a normal distribution. Values of these statistics outside
the range of -2 to +2 indicate significant departures from normality, which would tend
to invalidate any statistical test regarding the standard deviation. In this case, the
standardized skewness value is not within the range expected for data from a normal
distribution. The standardized kurtosis value is within the range expected for data from
a normal distribution
Percentiles for P2O5
8.19% = 1.0
13.65% = 5.0
16.825% = 10.0
21.1% = 25.0
24.465% = 50.0
25.9% = 75.0
28.16% = 90.0
29.09% = 95.0
29.84% = 99.0
This above values shows sample percentiles for P2O5. The percentiles are values below
which specific percentages of the data are found.
36
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
8
12
16
20
24
28
32
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART I)
Frequency Tabulation
for P2O5 Frequency tabulation for P2O5 (PART I)
Table 4.1:
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0
5.0
2.5
0
0.0000
0
0.0000
2
5.0
10.0
7.5
1
0.0143
1
0.0143
3
10.0
15.0
12.5
3
0.0429
4
0.0571
4
15.0
20.0
17.5
10
0.1429
14
0.2000
5
20.0
25.0
22.5
25
0.3571
39
0.5571
6
25.0
30.0
27.5
31
0.4429
70
1.0000
7
30.0
35.0
32.5
0
0.0000
70
1.0000
8
35.0
40.0
37.5
0
0.0000
70
1.0000
above
40.0
0
0.0000
70
1.0000
-------------------------------------------------------------------------------Mean = 23.1889
Standard deviation = 4.59995
Histogram for P2O5
frequency
The StatAdvisor
40
--------------This option performs a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
30
values in each interval. The frequencies show the number of data
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
20
intervals by pressing the alternate mouse button and selecting Pane
Options. You can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
10
0
0
10
20
30
40
P2O5
Figure 4.2.b:
Histogram for P2O5 (PART I)
37
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.2.1.2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 70
= 0.683571
= 0.115342
= 0.339621
= 0.15
= 1.55
= 2.21918
= -0.0326775
Percentiles for “t”
1.0% = 0.15
5.0% = 0.25
10.0% = 0.275
25.0% = 0.4
50.0% = 0.65
75.0% = 0.9
90.0% = 1.2
95.0% = 1.4
99.0% = 1.55
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.4
0.8
1.2
1.6
t
Figure 4.2.1:
Quantile plot for “t” (PART I)
38
Chapter 4
Sampling Data and Preliminary Statistical Analysis
tabulation for “t” (PART I)
Table 4.1:Frequency
Frequency Tabulation
for t
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0
0.225
0.1125
3
0.0429
3
0.0429
2
0.225
0.45
0.3375
19
0.2714
22
0.3143
3
0.45
0.675
0.5625
15
0.2143
37
0.5286
4
0.675
0.9
0.7875
19
0.2714
56
0.8000
5
0.9
1.125
1.0125
6
0.0857
62
0.8857
6
1.125
1.35
1.2375
3
0.0429
65
0.9286
7
1.35
1.575
1.4625
5
0.0714
70
1.0000
8
1.575
1.8
1.6875
0
0.0000
70
1.0000
above
1.8
0
0.0000
70
1.0000
-------------------------------------------------------------------------------Mean = 0.683571
Standard deviation = 0.339621
Histogram for t
frequency
The StatAdvisor
--------------20 performs a frequency tabulation by dividing the range
This option
of t into equal width intervals and counting the number of data values
in each interval.
The frequencies show the number of data values in
16
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
12alternate mouse button and selecting Pane Options. You
pressing the
can see the results of the tabulation graphically by selecting
Frequency Histogram
from the list of Graphical Options.
8
4
0
0
0.3
0.6
0.9
1.2
1.5
1.8
t
Figure 4.2.b:
Histogram for “t” (PART I)
4.2.2 Summary Statistics for Part I. a
4.2.2.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 26
= 23.8912
= 20.1703
= 4.49114
= 10.93
= 29.61
= -2.95294
= 1.90069
39
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Percentiles for P2O5
1.0% = 10.93
5.0% = 15.17
10.0% = 15.82
25.0% = 22.75
50.0% = 25.27
75.0% = 26.78
90.0% = 28.16
95.0% = 28.59
99.0% = 29.61
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
10
14
18
22
26
30
P2O5
Figure 4.2.1:
Table 4.1:
Quantile plot for P2O5 (PART I. a)
Frequency tabulation for P2O5 (PART I. a)
Frequency Tabulation for P2O5
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
9.0
0
0.0000
0
0.0000
1
9.0
13.0
11.0
1
0.0385
1
0.0385
2
13.0
17.0
15.0
2
0.0769
3
0.1154
3
17.0
21.0
19.0
3
0.1154
6
0.2308
4
21.0
25.0
23.0
6
0.2308
12
0.4615
5
25.0
29.0
27.0
13
0.5000
25
0.9615
6
29.0
33.0
31.0
1
0.0385
26
1.0000
above
33.0
0
0.0000
26
1.0000
-------------------------------------------------------------------------------Mean = 23.8912
Standard deviation = 4.49114
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
values in each interval. The frequencies show the number of data
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
intervals by pressing the alternate mouse button and selecting Pane
Options. You can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
40
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Histogram for P2O5
frequency
15
12
9
6
3
0
9
13
17
21
25
29
33
P2O5
Figure 4.2.b:
Histogram for P2O5 (PART I. a)
4 2 2 2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 26
= 0.623077
= 0.0568462
= 0.238424
= 0.2
= 1.4
= 2.19328
= 3.61473
Percentiles for “t”
1.0% = 0.2
5.0% = 0.3
10.0% = 0.3
25.0% = 0.45
50.0% = 0.65
75.0% = 0.75
90.0% = 0.8
95.0% = 0.9
99.0% = 1.4
41
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.1:
Quantile plot for “t” (PART I. a)
Frequency Tabulation
Table 4.1: for tFrequency
tabulation for “t” (PART I. a)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0
0.25
0.125
1
0.0385
1
0.0385
2
0.25
0.5
0.375
7
0.2692
8
0.3077
3
0.5
0.75
0.625
13
0.5000
21
0.8077
4
0.75
1.0
0.875
4
0.1538
25
0.9615
5
1.0
1.25
1.125
0
0.0000
25
0.9615
6
1.25
1.5
1.375
1
0.0385
26
1.0000
above
1.5
0
0.0000
26
1.0000
-------------------------------------------------------------------------------Mean = 0.623077
Standard deviation = 0.238424
Histogram for t
frequency
15
The StatAdvisor
--------------This option
12 performs a frequency tabulation by dividing the range
of t into equal width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
9 while the relative frequencies show the proportions in
each interval,
each interval. You can change the definition of the intervals by
pressing the 6alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram from the list of Graphical Options.
3
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.b:
Histogram for “t” (PART I. a)
42
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.2.3 Summary Statistics for Part I. b
4.2.3.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 32
= 23.9041
= 16.0579
= 4.00723
= 10.67
= 29.47
= -2.96259
= 2.80511
Percentiles for P2O5
10.67 = %1.0
17.33 = %5.0
19.23 = %10.0
21.49 = %25.0
25.3 = %50.0
26.28 = %75.0
28.16 = %90.0
29.04 = %95.0
29.47 = %99.0
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
10
14
18
22
26
30
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART I.b)
43
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Frequency Tabulation
P2O5
Table 4.1: for Frequency
tabulation for P2O5 (PART I.b)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
9.0
0
0.0000
0
0.0000
1
9.0
12.4286
10.7143
1
0.0313
1
0.0313
2
12.4286
15.8571
14.1429
0
0.0000
1
0.0313
3
15.8571
19.2857
17.5714
3
0.0938
4
0.1250
4
19.2857
22.7143
21.0
7
0.2188
11
0.3438
5
22.7143
26.1429
24.4286
13
0.4063
24
0.7500
6
26.1429
29.5714
27.8571
8
0.2500
32
1.0000
7
29.5714
33.0
31.2857
0
0.0000
32
1.0000
above
33.0
0
0.0000
32
1.0000
-------------------------------------------------------------------------------Mean = 23.9041
Standard deviation = 4.00723
Histogram for P2O5
15
frequency
The StatAdvisor
--------------This option
12 performs a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
values in each interval. The frequencies show the number of data
9
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
intervals by 6pressing the alternate mouse button and selecting Pane
Options. You can see the results of the tabulation graphically by
selecting Frequency
Histogram from the list of Graphical Options.
3
0
9
13
17
21
25
29
33
P2O5
Figure 4.2.b:
Histogram for. P2O5 (PART I.b)
4.2.3.2.Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 32
= 0.767188
= 0.129131
= 0.359347
= 0.15
= 1.55
= 0.529676
= -0.367043
44
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Percentiles for “t”
0.15 = %1.0
0.2 = %5.0
0.25 = %10.0
0.5 = %25.0
0.775 = %50.0
0.975 = %75.0
1.25 = %90.0
1.4 = %95.0
1.55 = %99.0
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.4
0.8
1.2
1.6
t
Figure 4.2.1:
Quantile plot for “t” (PART I.b)
Frequency Tabulation
Table 4.1: for tFrequency
tabulation for “t” (PART I.b)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0 0.257143 0.128571
4
0.1250
4
0.1250
2 0.257143 0.514286 0.385714
5
0.1563
9
0.2813
3 0.514286 0.771429 0.642857
7
0.2188
16
0.5000
4 0.771429
1.02857
0.9
11
0.3438
27
0.8438
5
1.02857
1.28571
1.15714
2
0.0625
29
0.9063
6
1.28571
1.54286
1.41429
2
0.0625
31
0.9688
7
1.54286
1.8
1.67143
1
0.0313
32
1.0000
above
1.8
0
0.0000
32
1.0000
-------------------------------------------------------------------------------Mean = 0.767188
Standard deviation = 0.359347
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of t into equal width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
pressing the alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram from the list of Graphical Options.
45
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Histogram for t
frequency
12
10
8
6
4
2
0
0
0.3
0.6
0.9
1.2
1.5
1.8
t
Figure 4.2.b:
Histogram for.”t” (PART I.b)
4.2.4 Summary Statistics for Part I.c
4.2.4.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 26
= 22.1931
= 21.8602
= 4.67549
= 8.19
= 29.84
= -2.3425
= 2.26453
Percentiles for P2O5
1.0% = 8.19
5.0% = 13.65
10.0% = 16.32
25.0% = 19.47
50.0% = 22.96
75.0% = 25.35
90.0% = 27.0
95.0% = 29.09
99.0% = 29.84
46
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for p2o5
proportion
1
0.8
0.6
0.4
0.2
0
8
12
16
20
24
28
32
p2o5
Figure 4.2.1:
Quantile plot for P2O5 (PART I.c)
Frequency Tabulation
Table 4.1: for p2o5
Frequency
tabulation for P2O5 (PART I.c)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0
6.66667
3.33333
0
0.0000
0
0.0000
2
6.66667
13.3333
10.0
1
0.0385
1
0.0385
3
13.3333
20.0
16.6667
6
0.2308
7
0.2692
4
20.0
26.6667
23.3333
16
0.6154
23
0.8846
5
26.6667
33.3333
30.0
3
0.1154
26
1.0000
6
33.3333
40.0
36.6667
0
0.0000
26
1.0000
above
40.0
0
0.0000
26
1.0000
-------------------------------------------------------------------------------Mean = 22.1931
Standard deviation = 4.67549
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of p2o5 into equal width intervals and counting the number of data
values in each interval. The frequencies show the number of data
16
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
intervals by pressing the alternate mouse button and selecting Pane
12
Options. You can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
frequency
Histogram for p2o5
8
4
0
0
10
20
30
40
p2o5
Figure 4.2.b:
Histogram for. P2O5 (PART I.c)
47
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4 2.4 2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 26
= 0.611538
= 0.134662
= 0.366963
= 0.2
= 1.5
= 2.06124
= 0.260786
Percentiles for “t”
0.2 = %1.0
0.25 = %5.0
0.25 = %10.0
0.3 = %25.0
0.5 = %50.0
0.85 = %75.0
1.2 = %90.0
1.4 = %95.0
1.5 = %99.0
Quantile Plot for T
proportion
1
0.8
0.6
0.4
0.2
0
0
0.3
0.6
0.9
1.2
1.5
T
Figure 4.2.1:
Quantile plot for “t” (PART I.c)
48
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Frequency Tabulation
Table 4.1: for TFrequency
tabulation for “t” (PART I.c)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0 0.266667 0.133333
5
0.1923
5
0.1923
2 0.266667 0.533333
0.4
9
0.3462
14
0.5385
3 0.533333
0.8 0.666667
5
0.1923
19
0.7308
4
0.8
1.06667 0.933333
4
0.1538
23
0.8846
5
1.06667
1.33333
1.2
1
0.0385
24
0.9231
6
1.33333
1.6
1.46667
2
0.0769
26
1.0000
above
1.6
0
0.0000
26
1.0000
-------------------------------------------------------------------------------Mean = 0.611538
Standard deviation = 0.366963
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of T into equal width intervals and counting the number of data values
in
10 each interval. The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
8
pressing the alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
6
Frequency
Histogram from the list of Graphical Options.
frequency
Histogram for T
4
2
0
0
0.4
0.8
1.2
1.6
T
Figure 4.2.b:
4.3
Histogram for.”t” (PART I.c)
Summary Statistics for Area II
4.3.1 Summary Statistics for whole area
4.3.1.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 123
= 22.8336
= 16.1922
= 4.02395
= 11.28
= 31.1
= -1.21595
= -0.39346
49
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Percentiles for P2O5
12.89 = %1.0
16.0 = %5.0
17.09 = %10.0
20.55 = %25.0
23.12 = %50.0
25.32 = %75.0
27.71 = %90.0
29.35 = %95.0
30.35 = %99.0
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
11
15
19
23
27
31
35
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART II)
Frequency Tabulation
Table 4.1: for P2O5
Frequency
tabulation for P2O5 (PART II)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
10.0
0
0.0000
0
0.0000
1
10.0
13.0
11.5
2
0.0163
2
0.0163
2
13.0
16.0
14.5
5
0.0407
7
0.0569
3
16.0
19.0
17.5
16
0.1301
23
0.1870
4
19.0
22.0
20.5
25
0.2033
48
0.3902
5
22.0
25.0
23.5
40
0.3252
88
0.7154
6
25.0
28.0
26.5
23
0.1870
111
0.9024
7
28.0
31.0
29.5
11
0.0894
122
0.9919
8
31.0
34.0
32.5
1
0.0081
123
1.0000
above
34.0
0
0.0000
123
1.0000
-------------------------------------------------------------------------------Mean = 22.8336
Standard deviation = 4.02395
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
values in each interval. The frequencies show the number of data
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
intervals by pressing the alternate mouse button and selecting Pane
Options. You can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
50
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Histogram for P2O5
frequency
40
30
20
10
0
10
14
18
22
26
30
34
P2O5
Figure 4.2.b:
Histogram for. P2O5 (PART II)
4.3.1.2. Summary Statistics for "t"
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 123
= 0.602033
= 0.109482
= 0.33088
= 0.1
= 2.05
= 7.27373
= 7.49626
Percentiles for “t”
0.15 = %1.0
0.2 = %5.0
0.3 = %10.0
0.4 = %25.0
0.55 = %50.0
0.7 = %75.0
1.05 = %90.0
1.3 = %95.0
1.65 = %99.0
51
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.4
0.8
1.2
1.6
2
2.4
t
Figure 4.2.1:
Quantile plot for “t” (PART II)
Frequency Tabulation
Table 4.1: for t Frequency
tabulation for “t” (PART II)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0
0.3
0.15
19
0.1545
19
0.1545
2
0.3
0.6
0.45
64
0.5203
83
0.6748
3
0.6
0.9
0.75
22
0.1789
105
0.8537
4
0.9
1.2
1.05
9
0.0732
114
0.9268
5
1.2
1.5
1.35
7
0.0569
121
0.9837
6
1.5
1.8
1.65
1
0.0081
122
0.9919
7
1.8
2.1
1.95
1
0.0081
123
1.0000
8
2.1
2.4
2.25
0
0.0000
123
1.0000
above
2.4
0
0.0000
123
1.0000
-------------------------------------------------------------------------------Mean = 0.602033
Standard deviation = 0.33088
Histogram for t
frequency
The StatAdvisor
80
--------------This option performs a frequency tabulation by dividing the range
of t into equal
60 width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
each interval.
40 You can change the definition of the intervals by
pressing the alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram
from the list of Graphical Options.
20
0
0
0.5
1
1.5
2
2.5
t
Figure 4.2.b:
Histogram for.”t” (PART II)
52
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.3.2 Summary Statistics for Part II.d
4.3.2.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 30
= 25.1037
= 13.3617
= 3.65536
= 18.17
= 31.1
= -1.1176
= -0.517068
Percentiles for P2O5
1.0% = 18.17
5.0% = 18.35
10.0% = 18.75
25.0% = 23.63
50.0% = 25.67
75.0% = 27.55
90.0% = 29.765
95.0% = 30.35
99.0% = 31.1
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
18
21
24
27
30
33
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART II.d)
53
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Frequency Tabulation
for P2O5 Frequency
Table 4.1:
tabulation for P2O5 (PART II.d)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
17.0
0
0.0000
0
0.0000
1
17.0
19.5
18.25
4
0.1333
4
0.1333
2
19.5
22.0
20.75
2
0.0667
6
0.2000
3
22.0
24.5
23.25
4
0.1333
10
0.3333
4
24.5
27.0
25.75
11
0.3667
21
0.7000
5
27.0
29.5
28.25
6
0.2000
27
0.9000
6
29.5
32.0
30.75
3
0.1000
30
1.0000
above
32.0
0
0.0000
30
1.0000
-------------------------------------------------------------------------------Mean = 25.1037
Standard deviation = 3.65536
Histogram for P2O5
frequency
The StatAdvisor 10
--------------This option performs
a frequency tabulation by dividing the range
8
of P2O5 into equal width intervals and counting the number of data
values in each interval. The frequencies show the number of data
6
values in each interval,
while the relative frequencies show the
proportions in each interval. You can change the definition of the
intervals by pressing
the alternate mouse button and selecting Pane
4
Options. You can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
2
0
17
20
23
26
29
32
P2O5
Figure 4.2.b:
Histogram for. P2O5 (PART II.d)
4.3.2.2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 27
= 0.762963
= 0.182806
= 0.427558
= 0.15
= 2.05
= 2.3748
= 1.91188
54
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Percentiles for "t"
0.15% = 1.0
0.2% = 5.0
0.25% = 10.0
0.5% = 25.0
0.7% = 50.0
0.95% = 75.0
1.4% = 90.0
1.4% = 95.0
2.05% = 99.0
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.4
0.8
1.2
1.6
2
2.4
t
Quantile plot for "t”(PART II.d)
Figure 4.2.1:
Table 4.1:
Frequency tabulation for “t” (PART II.d)
Frequency Tabulation for t
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0
0.4
0.2
4
0.1481
4
0.1481
2
0.4
0.8
0.6
14
0.5185
18
0.6667
3
0.8
1.2
1.0
5
0.1852
23
0.8519
4
1.2
1.6
1.4
3
0.1111
26
0.9630
5
1.6
2.0
1.8
0
0.0000
26
0.9630
6
2.0
2.4
2.2
1
0.0370
27
1.0000
above
2.4
0
0.0000
27
1.0000
-------------------------------------------------------------------------------Mean = 0.762963
Standard deviation = 0.427558
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of t into equal width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
pressing the alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram from the list of Graphical Options.
55
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Histogram for t
frequency
15
12
9
6
3
0
0
0.5
1
1.5
2
2.5
t
Figure 4.2.b:
Histogram for.”t”(PART II.d)
4.3.3 Summary Statistics for Part II.e.
4.3.3.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 35
= 21.65
= 11.2193
= 3.34952
= 15.43
= 27.71
= -0.381436
= -0.87217
Percentiles for P2O5
15.43% = 1.0
16.34% = 5.0
16.66% = 10.0
18.17% = 25.0
21.87% = 50.0
24.11% = 75.0
25.21% = 90.0
27.58% = 95.0
27.71% = 99.0
56
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
15
18
21
24
27
30
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART II.e)
Frequency Tabulation
for P2O5Frequency
Table 4.1:
tabulation for P2O5 (PART II.e)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
14.0
0
0.0000
0
0.0000
1
14.0
16.1429
15.0714
1
0.0286
1
0.0286
2
16.1429
18.2857
17.2143
8
0.2286
9
0.2571
3
18.2857
20.4286
19.3571
1
0.0286
10
0.2857
4
20.4286
22.5714
21.5
10
0.2857
20
0.5714
5
22.5714
24.7143
23.6429
9
0.2571
29
0.8286
6
24.7143
26.8571
25.7857
3
0.0857
32
0.9143
7
26.8571
29.0
27.9286
3
0.0857
35
1.0000
above
29.0
0
0.0000
35
1.0000
-------------------------------------------------------------------------------Mean = 21.65
Standard deviation = 3.34952
Histogram for P2O5
10
frequency
The StatAdvisor
--------------8
This option performs
a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
values in each interval.
The frequencies show the number of data
6
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
4
intervals by pressing the alternate mouse button and selecting Pane
Options. You can see the results of the tabulation graphically by
selecting Frequency
2 Histogram from the list of Graphical Options.
0
14
17
20
23
26
29
P2O5
Figure 4.2.b:
Histogram for.
P2O5 (PART II.e)
57
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.3.3.2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 32
= 0.546875
= 0.0441835
= 0.210199
= 0.2
= 1.25
= 3.15585
= 3.60273
Percentiles for "t"
0.2 = %1.0
0.25 = %5.0
0.35 = %10.0
0.425 = %25.0
0.55 = %50.0
0.65 = %75.0
0.8 = %90.0
0.95 = %95.0
1.25 = %99.0
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.1:
Quantile plot for “t”(PART II.e)
58
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Frequency
Tabulation
for
t
Table
4.1:
Frequency
tabulation for “t”(PART II.e)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0 0.214286 0.107143
1
0.0313
1
0.0313
2 0.214286 0.428571 0.321429
7
0.2188
8
0.2500
3 0.428571 0.642857 0.535714
15
0.4688
23
0.7188
4 0.642857 0.857143
0.75
6
0.1875
29
0.9063
5 0.857143
1.07143 0.964286
2
0.0625
31
0.9688
6
1.07143
1.28571
1.17857
1
0.0313
32
1.0000
7
1.28571
1.5
1.39286
0
0.0000
32
1.0000
above
1.5
0
0.0000
32
1.0000
-------------------------------------------------------------------------------Mean = 0.546875
Standard deviation = 0.210199
Histogram for t
frequency
15
The StatAdvisor
--------------This12
option performs a frequency tabulation by dividing the range
of t into equal width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
9
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
pressing6 the alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram from the list of Graphical Options.
3
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.b:
Histogram for.
“t”(PART II.e)
4.3.4 Summary Statistics for Part II.f.
4.3.4.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 32
= 21.7206
= 25.9008
= 5.08929
= 11.28
= 30.2
= -0.380872
= -0.981406
59
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Percentiles for P2O5
11.28% = 1.0
12.89% = 5.0
15.73% = 10.0
17.125% = 25.0
21.965% = 50.0
25.49% = 75.0
27.71% = 90.0
30.06% = 95.0
30.2% = 99.0
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
11
15
19
23
27
31
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART II.f)
Frequency Tabulation for P2O5
Table 4.1:
Frequency tabulation for P2O5 (PART II.f)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
10.0
0
0.0000
0
0.0000
1
10.0
13.4286
11.7143
2
0.0625
2
0.0625
2
13.4286
16.8571
15.1429
5
0.1563
7
0.2188
3
16.8571
20.2857
18.5714
5
0.1563
12
0.3750
4
20.2857
23.7143
22.0
7
0.2188
19
0.5938
5
23.7143
27.1429
25.4286
7
0.2188
26
0.8125
6
27.1429
30.5714
28.8571
6
0.1875
32
1.0000
7
30.5714
34.0
32.2857
0
0.0000
32
1.0000
above
34.0
0
0.0000
32
1.0000
-------------------------------------------------------------------------------Mean = 21.7206
Standard deviation = 5.08929
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
values in each interval. The frequencies show the number of data
values in each interval, while the relative frequencies show the
proportions in each interval. You can change the definition of the
intervals by pressing the alternate mouse button and selecting Pane
Options. You can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
60
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Histogram for P2O5
frequency
8
6
4
2
0
10
14
18
22
26
30
34
P2O5
Figure 4.2.b:
Histogram for.
P2O5 (PART II.f)
4.3.4.2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 32
= 0.546875
= 0.0441835
= 0.210199
= 0.2
= 1.25
= 3.15585
= 3.60273
Percentiles for t
0.2 = %1.0
0.25 = %5.0
0.35 = %10.0
0.425 = %25.0
0.55 = %50.0
0.65 = %75.0
0.8 = %90.0
0.95 = %95.0
1.25 = %99.0
61
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.1:
Quantile plot for “t” (PART II.f)
Frequency Tabulation
Table 4.1: for t Frequency
tabulation for “t” (PART II.f)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0 0.214286 0.107143
1
0.0313
1
0.0313
2 0.214286 0.428571 0.321429
7
0.2188
8
0.2500
3 0.428571 0.642857 0.535714
15
0.4688
23
0.7188
4 0.642857 0.857143
0.75
6
0.1875
29
0.9063
5 0.857143
1.07143 0.964286
2
0.0625
31
0.9688
6
1.07143
1.28571
1.17857
1
0.0313
32
1.0000
7
1.28571
1.5
1.39286
0
0.0000
32
1.0000
above
1.5
0
0.0000
32
1.0000
-------------------------------------------------------------------------------Mean = 0.546875
Standard deviation = 0.210199
Histogram for t
frequency
The StatAdvisor
15
--------------This option performs a frequency tabulation by dividing the range
of t into equal
12 width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
9
each interval. You can change the definition of the intervals by
pressing the alternate mouse button and selecting Pane Options. You
6
can see the results
of the tabulation graphically by selecting
Frequency Histogram from the list of Graphical Options.
3
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.b:
Histogram for.
“t” (PART II.f)
62
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.3.5 Summary Statistics for Part II.g.
4.3.5.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 38
= 22.935
= 12.4164
= 3.52369
= 15.85
= 29.91
= -0.205003
= -0.449807
Percentiles for P2O5
15.85 = %1.0
16.0 = %5.0
17.91 = %10.0
20.79 = %25.0
23.185 = %50.0
25.04 = %75.0
28.25 = %90.0
29.35 = %95.0
29.91 = %99.0
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
15
18
21
24
27
30
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART II.g)
63
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Frequency Tabulation for P2O5
Table 4.1:
Frequency tabulation for P2O5 (PART II.g)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
15.0
0
0.0000
0
0.0000
1
15.0
17.2857
16.1429
2
0.0526
2
0.0526
2
17.2857
19.5714
18.4286
4
0.1053
6
0.1579
3
19.5714
21.8571
20.7143
8
0.2105
14
0.3684
4
21.8571
24.1429
23.0
12
0.3158
26
0.6842
5
24.1429
26.4286
25.2857
6
0.1579
32
0.8421
6
26.4286
28.7143
27.5714
4
0.1053
36
0.9474
7
28.7143
31.0
29.8571
2
0.0526
38
1.0000
above
31.0
0
0.0000
38
1.0000
-------------------------------------------------------------------------------Mean = 22.935
Standard deviation = 3.52369
Histogram for P2O5
frequency
The StatAdvisor
12
--------------This option
10 performs a frequency tabulation by dividing the range
of P2O5 into equal width intervals and counting the number of data
values in each8 interval. The frequencies show the number of data
values in each interval, while the relative frequencies show the
proportions in6 each interval. You can change the definition of the
intervals by pressing the alternate mouse button and selecting Pane
Options. You 4can see the results of the tabulation graphically by
selecting Frequency Histogram from the list of Graphical Options.
2
0
15
19
23
27
31
P2O5
Figure 4.2.b:
Histogram for.
P2O5 (PART II.g)
4.3.5.2 Summary Statistics for “t”
Count = 38
Average = 0.618421
Variance = 0.0854569
Standard deviation = 0.29233
Minimum = 0.3
Maximum = 1.65
Stnd. skewness = 4.54245
Stnd. kurtosis = 4.83634
64
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Percentiles for "t"
0.3% = 1.0
0.3% = 5.0
0.35% = 10.0
0.45% = 25.0
0.55% = 50.0
0.78% = 75.0
1.0% = 90.0
1.4% = 95.0
1.65% = 99.0
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.3
0.6
0.9
1.2
1.5
1.8
t
Quantile plot for “t” (PART II.g)
Figure 4.2.1:
Frequency Tabulation for t
Table 4.1:
Frequency tabulation for “t” (PART II.g)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0 0.257143 0.128571
0
0.0000
0
0.0000
2 0.257143 0.514286 0.385714
18
0.4737
18
0.4737
3 0.514286 0.771429 0.642857
10
0.2632
28
0.7368
4 0.771429
1.02857
0.9
7
0.1842
35
0.9211
5
1.02857
1.28571
1.15714
1
0.0263
36
0.9474
6
1.28571
1.54286
1.41429
1
0.0263
37
0.9737
7
1.54286
1.8
1.67143
1
0.0263
38
1.0000
above
1.8
0
0.0000
38
1.0000
-------------------------------------------------------------------------------Mean = 0.618421
Standard deviation = 0.29233
The StatAdvisor
--------------This option performs a frequency tabulation by dividing the range
of t into equal width intervals and counting the number of data values
in each interval. The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
pressing the alternate mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram from the list of Graphical Options.
65
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Histogram for t
18
frequency
15
12
9
6
3
0
0
0.3
0.6
0.9
1.2
1.5
1.8
t
Figure 4.2.b:
Histogram for.
“t” (PART II.g)
4.3.6 Summary Statistics for Part II-h.
4.3.6.1 Summary Statistics for P2O5
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 19
= 23.1942
= 8.37586
= 2.89411
= 18.17
= 28.75
= 0.122484
= -0.449142
Percentiles for P2O5
1.0% = 18.17
5.0% = 18.17
10.0% = 18.75
25.0% = 21.09
50.0% = 23.08
75.0% = 24.96
90.0% = 27.53
95.0% = 28.75
99.0% = 28.75
66
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Quantile Plot for P2O5
proportion
1
0.8
0.6
0.4
0.2
0
18
20
22
24
26
28
30
P2O5
Figure 4.2.1:
Quantile plot for P2O5 (PART II.h)
Frequency Tabulation
forFrequency
P2O5
Table 4.1:
tabulation for P2O5 (PART II.h)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
17.0
0
0.0000
0
0.0000
1
17.0
19.5
18.25
3
0.1579
3
0.1579
2
19.5
22.0
20.75
3
0.1579
6
0.3158
3
22.0
24.5
23.25
5
0.2632
11
0.5789
4
24.5
27.0
25.75
6
0.3158
17
0.8947
5
27.0
29.5
28.25
2
0.1053
19
1.0000
6
29.5
32.0
30.75
0
0.0000
19
1.0000
above
32.0
0
0.0000
19
1.0000
-------------------------------------------------------------------------------Mean = 23.1942
Standard deviation = 2.89411
Histogram for P2O5
frequency
6
The StatAdvisor
--------------5 performs a frequency tabulation by dividing the range
This option
of P2O5 into equal width intervals and counting the number of data
4 interval. The frequencies show the number of data
values in each
values in each interval, while the relative frequencies show the
proportions3in each interval. You can change the definition of the
intervals by pressing the alternate mouse button and selecting Pane
2 can see the results of the tabulation graphically by
Options. You
selecting Frequency Histogram from the list of Graphical Options.
1
0
17
20
23
26
29
32
P2O5
Figure 4.2.b:
Histogram for.
P2O5 (PART II.h)
67
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.3.6.2 Summary Statistics for “t”
Count
Average
Variance
Standard deviation
Minimum
Maximum
Stnd. skewness
Stnd. kurtosis
= 19
= 0.663158
= 0.151345
= 0.389031
= 0.2
= 1.5
= 1.16173
= -0.369185
Percentiles for “t”
1.0% = 0.2
5.0% = 0.2
10.0% = 0.2
25.0% = 0.3
50.0% = 0.55
75.0% = 0.95
90.0% = 1.3
95.0% = 1.5
99.0% = 1.5
Quantile Plot for t
proportion
1
0.8
0.6
0.4
0.2
0
0
0.3
0.6
0.9
1.2
1.5
t
Figure 4.2.1:
Quantile plot for “t” (PART II.h)
68
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Frequency Tabulation for t
Table 4.1:
Frequency tabulation for “t” (PART II.h)
-------------------------------------------------------------------------------Lower
Upper
Relative
Cumulative Cum. Rel.
Class
Limit
Limit
Midpoint
Frequency Frequency Frequency
Frequency
-------------------------------------------------------------------------------at or below
0.0
0
0.0000
0
0.0000
1
0.0 0.266667 0.133333
4
0.2105
4
0.2105
2 0.266667 0.533333
0.4
4
0.2105
8
0.4211
3 0.533333
0.8 0.666667
5
0.2632
13
0.6842
4
0.8
1.06667 0.933333
3
0.1579
16
0.8421
5
1.06667
1.33333
1.2
2
0.1053
18
0.9474
6
1.33333
1.6
1.46667
1
0.0526
19
1.0000
above
1.6
0
0.0000
19
1.0000
-------------------------------------------------------------------------------Mean = 0.663158
Standard deviation = 0.389031
Histogram for t
frequency
The StatAdvisor
--------------5
This option performs
a frequency tabulation by dividing the range
of t into equal width intervals and counting the number of data values
in each interval.4 The frequencies show the number of data values in
each interval, while the relative frequencies show the proportions in
each interval. You can change the definition of the intervals by
3
pressing the alternate
mouse button and selecting Pane Options. You
can see the results of the tabulation graphically by selecting
Frequency Histogram
2 from the list of Graphical Options.
1
0
0
0.4
0.8
1.2
1.6
t
Figure 4.2.b:
Histogram for.
“t” (PART II.h)
69
Chapter 4
Sampling Data and Preliminary Statistical Analysis
4.4
Summery of the Statistical Analysis and Discussion
4.4.1
Analysis for the Overall Data
Table 4.15:
Variable
Mean
Variance
Ash
Carbon
Hydrogen
Moisture
Nitrogen
Oxygen
Sulphur
9.38053
68.7679
5.84211
4.27895
1.38684
8.27316
2.00947
16.6142
18.6876
0.106718
0.651721
0.611634
3.37975
0.55285
Table 4.16:
Summary statistics for the (PART I)
Standard
Deviation
4.07605
4.32292
0.32667
0.807292
0.78207
1.83841
0.743539
4.4.2
Mean
Variance
4.67
57.7
5.17
2.8
0.8
3.35
0.96
Standard
Kurtosis
0.945177
0.784183
0.049751
-0.349306
11.0293
4.0223
-0.903897
Summary statistics for the (PART II)
Standard
Deviation
7.85586 8.6074
2.93384
Ash
69.5872 5.49326
2.34377
Carbon
Hydrogen 5.78103 0.0744239 0.272807
1.28901
Moisture 4.31103 1.66156
Nitrogen 1.22655 0.0204163 0.142885
8.66586 1.93602
1.39141
Oxygen
2.5831 0.676529 0.822514
Sulphur
Variable
Standard
Skew
19.4 1.99284
75.58 -1.2759
6.49 -0.33116
5.8
-0.32108
4.34 5.94596
9.74 -4.01834
3.25 0.346857
Min. Max.
Standard
Skew
3.2
16.95 1.9997
63.85 74
-0.39216
5.33 6.6
1.7339
2.8
9.5
5.12851
0.95 1.43 -0.84904
2.68 10.63 -6.3754
1.39 4.85 2.32822
Min.
Max.
Standard
Kurtosis
2.13463
0.025317
1.75027
9.5931
-0.744281
13.3982
1.03893
Comments on the Results
Two boreholes have been excluded from the first round of data surveying those
were: (BH.Sand and BH.Conc.). The reason behind this decision was the
expected difficulties in area calculations and misleading results due to very
short distance between the boreholes. Statistical analysis of the different
variables has showing that the following boreholes (M3, M5, M5a and M13) at
the (PART I) do have missing data. In fact, the available data was provided
without core thickness at these boreholes. In the case of the (PART II) boreholes:
(K1, K2, and M13) had the same condition, i.e. provided with missing data.
The standardised Skewness and standardized Korusis parameters for Oxygen
and Nitrogen variables for the (PART I), are out of the accepted range (-2 to +2).
70
Chapter 4
Sampling Data and Preliminary Statistical Analysis
Also, these parameters for Oxygen and Moisture variables, from the (PART II),
are out of the accepted range, See Table 4.15 and Table 4.16.
71
Chapte
5.1
5
Results and Analysis
Introduction
Based on the statistical analysis for the chemical variables associated with the
borehole sampling at Mahamied area, and referring to the results in Chapter 4.
The actual sampling points that are suitable for estimation and analysis are 42
samples. Section 5.2 tabulates these data as X,Y and Z coordinates and thickness
of both the overburden and Phosphate seam.
Also the analysis of the Oxygen variable whether from (PART I) or (PART II)
has showed a non-linear distribution, and it has been decided to exclude it from
the further analysis.
This Chapter presents the results obtained from the Software for both (PART I)
and (PART II) for the following parameters: Average thickness, Total area,
Tonnage, and demonstrates the distribution of the following variables: Ash,
Carbon, and Sulphur. Results for the other variables (Hydrogen, Nitrogen,
Moisture) are shown in Appendix II. Section 5.3 shows the results obtained
using Triangular method, while section 5.4 illustrates the results of Ordinary
Kriging. All the results are introduced in the form of tables and contour maps.
Validation
5.2
of
No.
1
2
Software
is
explained
in
Section
5.5.
Original Sampling Data for Mahamied Phosphate Mine
Table 5.1:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
the
Original sampling data from Mahamied mine, (PART I)
Borehole
X, m
B1
140743.94
B10
138349.56
B12
138527.33
B16
138708.00
B2
139813.30
B3
139983.69
B3a
139618.31
B6a
139021.33
B7
139041.57
B9
138836.72
K1
139305.70
K2
139117.69
K3
138850.46
M1
138666.38
M10
137575.07
M11
136163.96
M12
135412.44
M14
134147.79
M15
137040.16
M16
136210.51
M17
133542.73
M18
136522.42
M19
135724.05
M2
138119.31
M21
136639.62
M21a
137216.33
M21b
137536.94
M22
135792.38
M23
135195.31
M25
136111.08
M4
138323.28
Y, m
1176265.65
1176831.04
1177846.81
1174969.00
1175667.11
1175452.57
1175046.93
1176764.27
1175830.13
1177310.10
1173481.83
1174305.66
1173920.16
1173177.70
1173191.28
1173193.10
1172620.16
1172143.41
1173614.17
1173795.41
1172798.53
1174346.31
1174410.09
1172768.20
1175814.20
1175545.04
1174998.73
1175129.77
1175081.10
1176277.45
1173686.01
Z, m
376.20
311.50
289.08
474.00
336.59
348.70
357.10
309.17
408.19
300.40
485.90
423.80
490.90
443.80
454.53
351.70
466.01
466.00
376.00
337.21
439.15
351.97
322.60
438.40
316.30
346.40
396.10
317.80
311.70
299.60
468.10
T11, m
130.10
360.20
474.25
253.35
088.29
052.73
051.37
302.63
256.00
382.05
116.80
000.00
185.26
049.65
151.10
139.10
256.75
262.43
154.60
186.33
340.24
262.48
292.63
046.50
383.35
324.60
300.17
399.15
417.79
464.78
185.30
T22, m
0.10
0.05
0.20
0.80
0.80
0.67
0.65
0.17
0.08
0.06
0.75
0.15
0.84
0.70
0.65
0.50
0.55
0.75
0.72
0.60
0.65
0.54
0.55
0.85
0.10
0.35
0.35
0.45
0.52
0.35
0.70
T1: Thickness of the Overburden
T2: Thickness of the Phosphate Seam
73
Chapter 5
No.
32
33
Results and Analysis
Borehole
X, m
M6
136512.28
M7
135146.48
Y, m
1172454.84
1171910.39
Table 5.1:
No.
34
35
36
37
38
39
40
41
Borehole
M8
M8a
M9
S2
S3
S3a
WW4
B15
X, m
134599.37
134377.35
138003.98
139462.10
140947.88
141560.55
139987.41
138288.45
Z, m
469.90
438.78
T11, m T22, m
139.25 0.70
153.26 0.84
Cont.
Y, m
1171453.44
1171815.84
1173373.99
1175234.84
1176356.39
1176094.34
1176267.43
1175839.96
Z, m
433.90
436.80
461.47
346.80
371.10
479.90
328.71
346.40
T1, m
109.70
173.45
148.30
085.32
077.50
069.15
140.50
269.70
T2, m
0.67
0.85
0.70
0.63
0.00
0.05
0.20
0.20
74
Chapter 5
Results and Analysis
Table 5.2:
Original sampling data from Mahamied mine, (PART II)
Figure 5.1:
A capture from the "O.R.E. Software" showing the values of the sampling points
(PART I)
Figure 5.2:
A capture from O.R.E Software showing the thickness of the boreholes (PART I)
5.3
Results of Triangular Method
The following steps are showing a numerical example showing how would the
average thickness from one triangle is calculated.
B15
M21b
B16
1. Calculating the lengths of the triangle sides based on the coordinates
Side (M21b – B16) = √ (∆x) ² + (∆y) ²
= √(1174998.73-1174969)² + (137536.94 -138708)² = 1171.437 m
75
Chapter 5
Results and Analysis
Side (M21b – B15) = 1128.023 m
Side (B15 – B16) = 966.744 m
2. Calculating the circumference of the triangle
Periphery =1171.437+1128.023 + 966.744 =3266.204 m
3. Calculating the area of the triangle
Area = √p(p- L1)(p- L2)(p- L3) = 503736.598 m2
Where:
p = Half periphery of triangle
L = Length of triangle side
4. Calculate the average thickness for the triangle
= (∑ Thickness / 3) = (1.84+1+1.32)/3 = 1.387
5. Calculating the volume under each triangle are
= Area * Average thickness = 1.387 * 503736.598 = 698514.749 m3
5.3.1
Upper Phosphate Seam
Table 5.3:
No.
1
2
3
4
5
6
7
8
9
10
11
3
4
Results of calculating the ore reserves from the (PART I) using O.R.E Software.
Triangle
B1-B3-WW4
B1-B3-S3a
B1-S3-WW4
B1-S3-S3a
B10-B12-B9
B10-B12-M25
B10-B6a-B9
B10-B6a-B15
B10-M25-B15
B12-B9-S3
B12-S3-S3a
Area, m2
0308236.33
0397103.84
0034505.27
0054518.08
0204840.01
1087684.57
0177172.91
0334929.06
1092341.44
0419006.17
0139415.25
AV. T1,
m
107.78
083.99
116.03
092.25
405.50
433.08
348.29
310.84
364.89
311.27
206.97
Volume13,
m3
033220684.05
033354075.47
004003761.81
005029292.55
083062623.45
471050806.94
061708141.55
104110466.42
398588107.99
130422654.89
028854308.94
AV. T2, Volume24,
m
m3
0.32
0099663.08
0.27
0108541.72
0.10
0003450.53
0.05
0002725.90
0.10
0021166.80
0.20
0217536.91
0.09
0016536.14
0.14
0046890.07
0.20
0218468.29
0.09
0036313.87
0.08
0011617.94
Volume1: Volume of the Overburden
Volume2: Volume of the Ore
76
Chapter 5
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Results and Analysis
B16-B3a-K2
B16-B3a-S2
B16-B7-S2
B16-B7-B15
B16-K2-M4
B16-M21b-B15
B16-M21b-M4
B2-B3-S2
B2-B3-WW4
B2-B7-S2
B2-B7-WW4
B3-B3a-S2
B3-B3a-K2
B3-K1-K2
B3-K1-S3a
B6a-B7-WW4
B6a-B7-B15
B6a-B9-WW4
B9-S3-WW4
K1-K2-K3
K1-K3-M1
K1-M1-M2
K2-K3-M4
K3-M1-M4
0317886.09
0091614.90
0280350.94
0325906.61
0390414.17
0503736.60
0756948.00
0074500.47
0069821.04
0195424.18
0245834.18
0066011.79
0033886.87
0464533.67
1336233.72
0446198.97
0351660.28
0217796.91
0551909.32
0146314.97
0209342.64
0047710.57
0070327.99
0174153.87
101.57
130.01
198.22
259.68
146.22
274.41
246.27
075.45
093.84
143.20
161.60
063.14
034.70
056.51
079.56
233.04
276.11
275.06
200.02
100.69
117.24
070.98
123.52
140.07
Table 5.3:
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
Triangle
M1-M2-M9
M1-M4-M9
M10-M15-M4
M10-M15-M6
M10-M2-M9
M10-M2-M6
M10-M4-M9
M11-M12-M6
M11-M12-M19
M11-M15-M16
M11-M15-M6
M11-M16-M19
M12-M14-M7
M12-M14-M17
M12-M17-M23
M12-M19-M23
Area, m2
0189318.59
0134678.72
0290523.28
0421686.19
0140450.67
0425222.65
0037744.60
0377191.81
0583317.18
0254071.61
0396765.26
0160806.54
0385407.10
0558479.93
2281257.33
0577750.51
AV. T1,
m
081.48
127.75
163.67
148.32
115.30
112.28
161.57
178.37
229.49
160.01
144.32
206.02
224.15
286.47
338.26
322.39
032288749.63
011911158.36
055572098.25
084632514.67
057085058.40
138228680.75
186416106.50
005620811.87
006552006.59
027985393.35
039725984.51
004167984.43
001175874.32
026250797.38
106310754.53
103983694.09
097096919.58
059907217.24
110391062.22
014731966.91
024542633.12
003386655.33
008686913.66
024393731.93
0.53
0.69
0.50
0.36
0.55
0.45
0.62
0.70
0.56
0.50
0.36
0.65
0.49
0.52
0.49
0.15
0.15
0.14
0.09
0.58
0.76
0.77
0.56
0.75
0169539.25
0063519.66
0141109.97
0117326.38
0214727.79
0226681.47
0466784.60
0052150.33
0038867.05
0098363.50
0088500.31
0042907.66
0016604.57
0243105.95
0654754.52
0066929.85
0052749.04
0031217.56
0047832.14
0084862.68
0159798.21
0036578.10
0039618.10
0130034.89
Cont.
Volume1,
m3
015426309.38
017205206.80
047548976.11
062543090.34
016193961.86
047745416.48
006098268.82
067278445.49
133867404.05
040653997.80
057259839.37
033129363.02
086387716.83
159989607.58
771658102.64
186260986.00
AV. T2, Volume2,
m
m3
0.75
0141988.94
0.70
0094275.11
0.69
0200461.06
0.69
0290963.47
0.73
0102997.16
0.73
0311829.94
0.68
0025792.14
0.58
0220028.56
0.53
0311102.50
0.61
0154136.78
0.64
0253929.77
0.55
0088443.60
0.71
0274923.73
0.65
0363011.96
0.57
1307920.87
0.54
0311985.27
77
Chapter 5
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
Results and Analysis
M12-M6-M7
M14-M17-M8
M14-M7-M8a
M14-M7-M8
M14-M8-M8a
M15-M16-M18
M15-M18-M21b
M15-M21b-M4
M16-M18-M19
M18-M19-M22
M18-M21-M22
M18-M21-M21b
M19-M22-M23
M2-M6-M8
M21-M21a-M25
M21-M21a-M21b
M21-M22-M25
M21a-M21b-B15
M21a-M25-B15
M22-M23-M25
M6-M7-M8
M7-M8-M8a
0412300.97
0060817.08
0136824.41
0291919.48
0005232.73
0256792.38
0540277.30
0870433.98
0229857.83
0289464.50
0581719.96
0706370.07
0213186.86
0504925.18
0062449.54
0114383.53
0377116.28
0340132.09
0555595.87
0334867.08
0163114.14
0149862.35
183.09
237.46
196.38
175.13
181.86
201.14
239.08
213.36
247.15
318.09
348.33
315.33
369.86
098.48
390.91
336.04
415.76
298.16
353.03
427.24
134.07
145.47
075486810.63
014441420.93
026869576.86
051123859.21
000951623.61
051650362.68
129171298.24
185712891.67
056808595.60
092074799.36
202628575.92
222742028.55
078848580.77
049726715.03
024412149.90
038437440.16
156789865.03
101412649.94
196140157.86
143068613.10
021868712.11
021800476.27
Number of triangles
Total area
Volume
Average thickness of (PART I)
Reserves
Average thickness of overburden
Volume of overburden
0.70
0.69
0.81
0.75
0.76
0.62
0.54
0.59
0.56
0.51
0.36
0.33
0.51
0.74
0.27
0.27
0.30
0.30
0.30
0.44
0.74
0.79
0287236.34
0041963.79
0111283.85
0219912.68
0003959.43
0159211.27
0289948.82
0513556.05
0129486.58
0148591.78
0211358.25
0233102.12
0108014.68
0373644.64
0016653.21
0030502.27
0113134.88
0102039.63
0166678.76
0147341.52
0120160.75
0117891.72
73
26030587.2m2
12166938.7m3
0.467m
17381340.9 ton
241.096m
6275863588m3
Beside the above results, the estimation of the thickness of the overburden or
the thickness of the Phosphate seam at any un-sampled point within the
selected triangulation net can be estimated using the O.R.E. Software.
The following are examples of some random points
Point
X, m
Y, m
1
134718.38
113346.81
T1 (PART I)
(Overburden), m
328.7
T2 (PART I),
m
0.576
78
Chapter 5
Results and Analysis
2
3
4
5
6
7
138091.27
137536.94
137040.16
137870.93
140125.16
136294.60
1174516.28
1174998.73
1173614.17
1176465.45
1175906.13
1175007.82
247.78
300.17
154.60
358.91
099.70
342.49
0.58
0.65
0.72
0.15
0.39
0.39
Point 3 refers to borehole M21b and point 4 refers to borehole M15
Table 5.5:
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Results of average assay calculations of the (PART I) using O.R.E. Software
Triangular
B16-B2-B15
B16-B2-K1
B16-K1-K3
B16-K1-M4
B16-K3-M4
B16-M4-B15
K1-K3-M4
K1-M2-M4
M10-M15-M4
M10-M15-M6
M10-M2-M9
M10-M2-M4
M10-M2-M6
M10-M4-M9
M14-M17-M8
M14-M17-M7
M14-M7-M8a
M14-M7-M8
M14-M8-M8a
M15-M16-M6
M15-M16-M19
M15-M19-M6
M15-M19-B15
M15-M4-B15
M16-M19-M6
M17-M19-M7
M17-M7-M8
M19-M6-M7
Carbon,
Ash, Hydrogen, Moisture, Sulphur,
A*Vol.
A*Vol.
A*Vol.
A*Vol.
A*Vol.
261295.5 030070.8 022328.1 016950.1 006118.8
551596.7 075157.2 046301.0 035552.8 015586.5
107782.5 019605.6 009125.0 007516.2 004308.8
337219.5 052911.2 028261.6 021937.1 010686.2
152716.4 023183.6 012939.1 010549.2 005243.9
167967.8 023580.6 014344.8 011033.4 004621.5
085766.8 013834.2 007064.6 005822.6 003246.2
245581.2 034419.4 020408.8 016744.0 008235.2
134785.4 023556.3 011624.6 008581.6 002588.0
194495.7 035470.4 016990.9 012652.7 004327.1
070014.2 009460.1 005899.9 005303.2 001743.7
147712.6 018293.2 012372.2 010717.8 003943.9
213291.7 027847.1 018080.5 015758.0 006301.1
017744.0 002297.6 001465.2 001256.6 000354.0
030400.4 002433.3 002635.8 001389.1 000710.7
141028.6 011268.0 011874.7 006974.3 002595.0
082282.6 005653.8 006910.2 004267.7 001791.3
162784.6 011394.6 013819.9 008003.3 003448.7
002887.0 000195.8 000248.9 000140.5 000076.7
238484.6 042834.8 020882.0 013648.9 007387.4
083285.8 020354.3 007439.4 005423.0 003105.8
408975.1 095135.2 036536.3 028261.8 013125.1
593204.9 166928.2 054412.9 041805.3 018894.8
499677.5 092076.5 043816.9 028972.2 010407.7
094302.1 017366.8 008071.7 006711.9 004106.8
1065490.4 149726.2 089360.9 069657.7 030906.9
321407.3 025349.9 026896.5 017194.0 008047.2
742853.7 109220.7 062301.1 052294.9 023373.8
79
Chapter 5
No.
29
30
31
32
Results and Analysis
Triangular
M2-M4-M9
M2-M6-M8
M6-M7-M8
M7-M8-M8a
Total Volume, m3
Average Assay
Carbon,
A*Vol.
059238.1
260984.7
087346.9
086813.1
7646425
67.90%
Ash, Hydrogen, Moisture, Sulphur,
A*Vol.
A*Vol.
A*Vol.
A*Vol.
007167.3 004955.7 004179.2 001552.6
027531.9 022414.8 016918.4 008877.8
007478.8 007309.6 005080.9 002384.3
005846.9 007249.0 004830.2 002425.6
1186941
10.54%
654282
5.81%
495497
4.40%
220722
1.96%
80
Chapter 5
Results and Analysis
thickness contour map of area I
805500
805000
804500
Y, m
804000
803500
803000
802500
802000
801500
801000
277000
278000
279000
280000
X, m
Figure 5.3:
Contour maps for Carbon, Ash and Sulphur of the (PART I) using the Triangular
method a) Plots using SURFER 7
b) Plots using O.R.E. Software
81
Chapter 5
5.3.2
Results and Analysis
Main Phosphate Seam
1176000
Y
1175000
1174000
1173000
1172000
135000
136000
137000
138000
139000
140000
141000
X
a) Carbon%
b) Carbon%
a) Ash%
b) Ash%
a) Sulphur%
b) Sulphur%
Figure 5.6:
Contour maps for Carbon, Ash and Sulphur of the (PART II), using the Triangular
method a) Plots using SURFER 7
b) Plots using O.R.E. Software
82
Chapter 5
5.4
Results and Analysis
Results of Ordinary Kriging Technique
Variowin 2.21 Software has been used to generate the variograms of all the
studied variables. Figure 5.7 Show and example using Carebon samples from
the (PART II).
Figure 5.7:
Outputs from Variowin showing the variograms of Carbon
83
Chapter 5
5.4.1
Results and Analysis
Upper Phosphate Seam
1177000
1176000
Y
1175000
1174000
1173000
1172000
134000
135000
136000
137000
138000
139000
140000
141000
X
Thickness, m
1177000
1176000
Y
1175000
1174000
1173000
1172000
134000
135000
136000
137000
138000
139000
140000
141000
X
Elevation, m
1177000
1176000
Y
1175000
1174000
1173000
1172000
134000
135000
136000
137000
138000
139000
140000
141000
X
Overburden, m
Figure 5.8:
Contour maps and 3D represention for the Thickness, Elevation and Overburden for
(PART I), calculated based on (OK)
84
Chapter 5
Results and Analysis
1175000
Y
1174000
1173000
1172000
134000
135000
136000
137000
138000
139000
X
Carbon %
1175000
Y
1174000
1173000
1172000
134000
135000
136000
137000
138000
139000
X
Ash %
1175000
Y
1174000
1173000
1172000
134000
135000
136000
137000
138000
139000
X
Sulphur %
Figure 5.9:
Contour maps and 3D representation for the Carbon, Ash and Sulphur for (PART I),
calculated based on (OK)
85
Chapter 5
Results and Analysis
Main Phosphate Seam
5.5
Validation of the Results
In order to examine the reliability of the developed Software, The results of ore
reserve estimation of the (PART II) are compared with the last report about the
same area and provided by The Ministry of Industry and Mining Projects,
Egypt, (1996).
Proved Ore Reserves of the (PART II) = 27 million tons (Report)
Calculated ore reserves using O.R.E Software = 26.62 million tons.
This close difference does not mean that the calculations done using the
developed software is correct rather than it just a hint of the correct way.
However, It is believed that the difference came from the high precision of the
method used in the O.R.E Software. Using the correct coordinates of the
sampling points will give more exact determination of the lengths than
measuring the lengths from the existing maps (low accuracy especially with the
small map scale).
Another way to check the quality of the developed Software is comparing the
visual results with one of the known Software’s (SURFER 7.0). Figures 5.3 and
5.6 showed how close is the two results.
86
Chapter
6.1
6
Some Useful Information to
MIS
Introduction
Like, other mining information, surface mining information and data, such as,
height of bench, type and shape of trench, drilling, blasting, machines, mining
methods, etc., need an efficient system to combine, access, manipulate, and
update, the information in a format that is easily accessible and readily
communicated to the authorities, researcher and investors.
The task in this chapter is to provide as much as possible useful information to
aid in building the MIS (Mining Information System), developed by B.Sc.
students at Mining and Metallurgical Engineering Department, Assiut
University. (El Mokadum and et al., 2003)
Chapter 6
Mining Information System (MIS)
At this point, the simple calculations of surface mining parameters were
calculated and made available in a digital format, so one can easily use them as
part of the MIS. The following sections are explaining how the information has
gathered.
6.2
Surface Mining Method
6.2.1
General
Essential factors for surface mine operation, Figure (6.1):
1. Choice of the site of mine taking into consideration the nearest
presence of the ore than solving the transportation system.
2. Development system and mining method.
3. Removal of the overburden according to the development scheme
and mining method also extraction of ore.
4. Loading and transportation to the place of storing.
Figure 6.1:
Surface mining pattern showing extraction and development (Digistar, 2004).
6.2.2 Advantages of surface mining
1.
2.
3.
4.
5.
6.
7.
Cost of extraction for one ton in surface less than underground.
No need for support and natural ventilation.
Economic flexibility of operation.
Drainage of water is easy than underground.
Sufficient light.
Used large power and high machines.
Greater productivity of labour at low cost.
88
Chapter 6
Mining Information System (MIS)
6.2.3 Disadvantages
1. Dependence up on climatic condition.
2. Considerable original out lay the purchase of equipment and
excavator of spoil.
3. Required large area for mining.
6.2.4 Factors favouring surface mining:
1.
2.
3.
4.
5.
6.
6.3
Higher productivity.
Greater out put per mine.
Greater consideration of all operation and of men and machine.
Lower operation cost per ton.
Lower capital cost per annual mine tonnage.
Greater geological certainty.
Surface or Underground Mining Methods?
One of the most important steps in mining development is to decide the most
appropriate mining method for ore extraction. This vital step always follows
the ore reserve estimation. Normally upon calculating the volumes of the
overburden and reserves, several approaches have to be examined to decide
Surface or Underground, Figure (6.2) shows the main factors in both methods.
Figure 6 2:
Main operations in Surface and Underground mining methods (Digistar, 2004)
89
Chapter 6
6.3.1
Mining Information System (MIS)
Calculation of Stripping Ratio
The stripping ratio can be calculated using one of the following formulae.
1.
Stripping Ratio =
Volume of overburden removed
Volume of mineral recovered
(6.1)
2.
Stripping Ratio =
Volume of overburden removed
Weight of mineral recovered
(6.2)
3.
Stripping Ratio =
Thickness of overburden removed
Thickness of mineral recovered
(6.3)
At El Mahamid area, the only available information is the volume of both the
overburden and the ore recovered, so equation (6.1) is used to determine the
stripping ratio as follows:
Volume of over burden removed = 12,000,000 m3
given by the Company.
Volume of mineral removed = 193637780.3 m3
Calculated in Chapter 4.
Stripping Ratio = 12000000/193637780.33 = 0.62
Since the stripping ratio is less than one, so for the given situation surface
mining method is preferable, Figure (6.3), shows the preparation of the area at
East Mahamid for extraction using surface mine technology. Note that the
thickness of the overburden is very small.
.
Figure 6 3:
Extraction of ore using surface mining, (taken from ElNasrmining.com).
90
Chapter 6
6.4
Mining Information System (MIS)
Height of bench
Height of bench can be calculated according to three considerations:
1) Stability of face slope.
2) The safety of the work place.
3) Efficiency of the work place.
6.4.1
Height of bench due to stability of the face slope
H
Where:
H
C
α
γ
4C
 sin 2
(6.4)
Vertical face height, m.
Force of cohesion, t/m2.
Slope angle of slip plane.
Volumetric weight of the material, t/m3
6.4.1.1
The Maximum height of the vertical face
Hv 
6.4.1.2
4C

(6.5)
,m
The limiting height of a vertical face
Hv 
2C. cos
 (1  sin  )
(6.6)
Where:
Φ = Angle of repose.
6.4.2 Height of bench due to safety of working place
H v ≤ H d max
(6.7)
Where:
Hdmax = Maximum digging of the excavation in meters.
6.4.3
Height of bench calculated from the efficiency of work place


sin  .sin 
H V  0.7a 

  (1   ) sin (    ) 
0.5
(6.8)
91
Chapter 6
Mining Information System (MIS)
Where:
a

Β
K

 
Rd
Rl

 
α
k
γ
6.5
Width of the broken down of material formed = 0.8 (Rd+Rl).
Slope angle of broken down material.
Slope angle of the face.
Loosening factor of the face material.
Ratio of length of least resistance line of first raw of blast holes to
face height.
Ratio of distance between rows of blast holes to length of line of
least resistance.
Digging radius = 13.40 m
Loading radius = 12.10 m
0.55 - 0.70
0.75 - 0.85
35
1.5
1.82 t/m3
Development schemes and mine trenches
Development and design of surface mining systems and trenches is generally
carried out for:


External, and/or
Internal.
In both cases, the classification of development schemes is mainly:



Separate trench.
Group trench.
Twin trenches.
6.5.1 Type of trenches
1) The capital trench.
2) The sectional trench.
3) The special trench.
Figure (6.4) shows different types of trenches
92
Chapter 6
Mining Information System (MIS)
Capital trench
Figure 6.4:
6.5.2
Sectional trench
Special trench
Type of trenches, (After, El-Abde Rassoul, 1978).
Shape of trenches:
Figure (6.5) shows the different shapes of the trenches. Those are:
1)
2)
3)
4)
5)
6)
Straight.
Loop.
Curved.
Dead lock.
Spiral.
Combination.
Figure 6.5:
Shape of Trenches.
Some of these shapes can be seen in Figure (6.6)
93
Chapter 6
Mining Information System (MIS)
Figure 6.6:
6.6
A picture showing the benches and trenches. (Reference)
Calculation of height of bench
The height of bench at El Mahamid phosphate mine has been calculated based
on the stability of face slope, using equation (6.4).
H
4 * 74
 86.5 m
1.82 * sin (2 * 70)
The maximum height of the vertical face, can be calculated from equation (6.5)
Hv 
4 * 74
 162 .63 m
1.82
The limiting height of the vertical face is determined from equation (6.6) as:
Hv 
2 * 74 * cos (45)
 196.32 m
1.82 (1  sin( 45))
Height of bench due to safety of working place is calculated using equation
(6.7) as:
H v ≤ 1.5*14 = 21 m
Height of bench calculated from the efficiency of work place:
Substitute at equation (5).
94
Chapter 6
Mining Information System (MIS)
H v  0.7 * 20.4 *
Where:
a
k
β
α
ή
ή
Rd
Rl
Hdmax
C
α
φ
6.7
sin 35 * sin 85
 15.36 m
1.5 * 0.55 1  0.75 sin 85  35
0.8 (13.8 + 12.1) = 20.4 m
1.5
85
35
0.55
0.75
13.4 m.
12.1 m.
15 m.
74 ton/m2
70
45
Drilling
Applying mechanical, thermal, and physico chemical, electric spark and other
methods can break up rock.
The purpose of drilling is to create large or small diameter holes in the natural
rock massive. The drilling of borehole is labor consuming and costly process
especially when drilling is done rather difficulty breaking rocks.
6.7.1
Method of borehole drilling
The two methods; rotary and percussion are still the basis of all conventional
drilling techniques.
6.7.1.1
Rotary blast hole diameter:
In rotary drilling, the disintegrations of the rock occur as a result of a
concurrent action on bit of a load (pressure) and of a torque. Under the
effect of the pressure, the bit penetrates the rock, while under that of the
torque it shears it. Rotary drilling can be employed in very soft material
95
Chapter 6
Mining Information System (MIS)
when drag bit are used, and in medium to very hard rock when rolling
cutter are used.
Most rotary blast holes are shallow, from (30 to 60) ft, and are in the (6 to 9)
in rang, although the rotary method is capable of drilling (3 to17) in holes.
Rotary drills used in open pit blast hole drilling consist of a power source, a
drill string composed of a single or connected series of hollow drill pipe,
and a drill bit.
6.7.1.2
Percussive blast hole drilling for surface mining
Percussive drills are most commonly used to drill small diameter holes in
hard rock and large diameter holes where heavy rotary rigs cannot be used
or are not available percussive drilling is employed for holes from (2 to 12)
inch in diameter to depth of 100 feet with surface drills. Figure (6.7) shows
how El Nasr mining company is using this method at El Mahamid
phosphate mine.
Figure 6.7:
Percussive drills for removing the ore at El Mahamid.
However, the Rotary drilling, (Figure 6.8), has several advantages, among them:


Rotary drilling is preferable in many sedimentary rocks.
Rotary drilling is an alternative in hard rock provided that the drill is
adequate size and large holes are acceptable.
96
Chapter 6


Mining Information System (MIS)
Rotary drilling gives a wide range of hole size and may be used to
greater depths.
Rotary drilling in bad ground may be the sole economic method.
Figure 6.8:
6.8
Drilling operation at the study area (ElNasrMining).
Blasting
Explosives can define as: Solid or liquid substance or mixture of substances which on
the application of suitable stimulus to a small portion of the mass is converted in a very
short interval of time into other more stable substances, largely or entirely gaseous,
with the development of very high temperature and pressure” (Abdel Erassoul, 1978).
The factors affecting the selection of the explosives are:
1) Explosives cost and properties.
2) Rock properties.
3) Working condition.
6.8.1
Calculation of burden and spacing for 4 inch. borehole diameter:
First method (Pearce formula)
B  K *d *
P
T
(6.9)
Where:
B Max. height of burden in inches.
K Constant depending on rock characteristics:
= 0.7 for strong rock.
= 1.0 for weak rock.
d = Borehole diameter.
P = Detonation pressure, gm/cm2
97
Chapter 6
Mining Information System (MIS)
T = Ultimate tensile strength of rock, gm/cm2
4.18 *107 *  vod 
P
1  0.8 
2

vod

gm/cm2
(6.10)
Density of explosives, gm/cm3
Velocity of detonation, ft/ sec.
0.84 gm/cm3 For ANFO.
For 4 inch borehole diameter vod = 11800 ft/ sec, and substitute at equation
(6.10):
4.18 *10 7 * 0.84 * 11800 
P
 29240 .4 gm / cm 2
1  0.8 * 0.84
2
For Phosphate; substitute in equation (6.9):
B  0.9 * 4 *
29240 .4
 3.64 m
18.473
S = 1.25 B
(6.11)
S = 1.25 * 3.64 = 4.55 m
S = Spacing between borehole.
6.8.2
Calculation of burden and spacing for 2 inch borehole diameter:
For 2 inch boreholes diameter vod = 9200 ft/sec, and substitute at equation
(6.10).
4.18 *10 7 * 0.84 * 9200 
P
 20410 .8 kg / cm 2
1  0.8 * 0.84
2
For Phosphate, Substitute at equation (6.9):
B  0 .9 * 4 *
20410 .8
 3.04 m
18.473
S = 1.25 B
S = 1.25 * 3.04 = 3.8 m.
98
Chapter 6
6.9
Mining Information System (MIS)
Loading and Unloading
Bench level intervals are to a large measure determined by the type of shovel or
loader used, and these are selected on the basis of the character of the ore and
the manner in which it breaks upon blasting and supports itself on the working
face (Randall, 1998). Figure (6.9) illustrates by sketches loading ore cars.
Figure 6.9:
Removing ore (After Randall, 1998).
99
Chapter 6
Mining Information System (MIS)
The loading and loading processes of the phosphate ores at Mahamid as well as
the overburden is carried out at the study area using different equipment such
as the trucks showing in Figure (6.10).
Figure 6.10:
Loading of phosphate at the extraction area of Mahamied, Picture taken in 2004.
6.10 Equipment
The following equipment is used at El Mahamid phosphate mine:
6.10.1 Trucks
Ore trucks are very large hauling trucks used to carry between 50-250 tons of
ore each load, see Figure (6.11). Usually those trucks are powerful enough to
climb steep inclines. The main purpose of using them is to move the broken
rock to a waste pile or mill depending on ore grade.
100
Chapter 6
Mining Information System (MIS)
Figure 6.11:
An Example of the trucks used at El Mahamid.
6.10.2 Drag Line Specifications
Drag line type 380 W, is a very important apparatus at East Sebaiya mines,
which use in the metallurgical industries, by removing over burden by open
cast mine. Figure (6.12) shows a picture taken at the study area. The
specification and capacity of the dragline is highly requested for the MIS.
Figure 6.12:
Dumping of the overburden at El Mahamid phosphate mine.
101
Chapter 6
Mining Information System (MIS)
102
Chapter 6
Mining Information System (MIS)
Figure 6.1:
A Diagram for the proposed Mining Information System (MIS)
103
Chapter
7.1
7
Conclusions and
Recommendations
Conclusions
The phosphate ore reserves at Eastern El Mahamid, Esna, Egypt, have been
estimated using 340 sampling points. The Triangular method is used as the
basic of the mathematical calculations of the average thickness, average assay
and estimation of the total volume and tonnage of the ore. The large number of
the boreholes require an accurate and fast way of calculations with minimum
risk of errors in calculations The students has chosen EXCEL software to carry
out most of the calculations, and another 3 Software’s for displaying the output
data in the form of contour maps and 3D representation of the variables under
study The main points reached at the end of this project are:
Chapter 7

Conclusions and Recommendations
A review of the geological and geophysical studies at the study area and
introducing new geological maps for the ore concentrate and types of
phosphate.

Estimating the tonnage of ore reserve at acquired area provided that
sufficient sampling boreholes are available.

Calculating the area and average thickness or Assay within any portion
of the entire area.

Determine the lengths between any two sampling points using their X
and Y coordinates.

Mapping the locations of the boreholes at the area.

Link the output data with Surfer Software for contouring the surfaces and
conducting a 3D representation of the thickness and P2O5 at the study
area.

An intensive study has been made over all the available data about the
study area in the Internet and introduced in a fore suitable for the MIS.

In one sentence; the average thickness of the phosphate ore at the study
area is estimated as 0.61 meter and the ore reserves as 44 million tons
with average P2O5 = 23%.
The dissertation has also introduced some useful information about the mining
operations at the study area that can be used for the database of the Egyptian
Mines (MIS), where the available information of Mahamied Phosphate Mine
has used as the second input record, followed El Maghara coal mine.
7.2
Recommendations

The introduced methodology is based on the Triangular method for ore
reserve estimation, using Excel software,. However, it is recommended
to test it on one or more of the following methods and techniques for
more accurate calculations such as: Kriging techniques (OK, SK, UK) or
Multiquadric technique.
105
Chapter 7

Conclusions and Recommendations
The calculations and gathered information about the area need more
work to maximize the benefit of using the MIS. Other data and
information require a field study and a good cooperation from the
company.

A questionnaire has to be designed and send to the other Egyptian
authorizations and mining companies to prepare and provide the
required information so that a complete database can be created (Mining
Information System for Egyptian Mines).
106
References
References
Atef et al, 1999 “A Study in the Structural and Building Materials in Red Sea
Governorate“, Mining & Metallurgical Engineering Department, Faculty of
Engineering, Assiut University. 128 P.
Ahmed El-Otify et al, 1997 “A Study on the Structural and Building Materials in
Kharga Oasis”, Mining & Metallurgical Engineering Department, Faculty of
Engineering, Assiut University. 132 P.
Moataz El-Nashar et al, 1997 “A Geostatistic Studies of Baharia Oasis Iron Ore”,
Mining & Metallurgical Engineering Department, Faculty of Engineering, Assiut
University. 54 P.
Carls Pavetto, “Surface Mine Blasting”, Mining Information Services Maclean Hunter
Publishing Company, 29 North Wacker Drive Chicago. 317 P.
Randall D. Peterson, P.E. and David A. Hettinger, 1998 “Softwall Mining:
New Technology for Phosphatic Clays and Other Deposits in Soft, Shallow
Conditions”, The Society for Mining Metallurgy and Exploration Annual Convention,
Orlando, Florida.
Mikhailov, L. A. et al, 1970 “Stratigraphy of the Phosphate-Bearing Cretaceous and
Paleogene Sediments of the Nile Valley between Idfu and Qena”, Studies on Some
Mineral Deposits of Egypt, by O. Moharram et al, Geol. Survey. Egypt, Article7. 109134 P.
Rushdi Said, 1968 “Report on the Results of Geological Exploration at The ElMahamid Phosphorite Deposit Carried out in 1966-1968”, Egyptian General
Organization For Geological Research and Mining. 154-173 P.
Abdel-Rassoul, E, I., 1978. “Studies on the Relations between the Properties of
Surface Mine Faces and Blasting Results” MSc Thesis, Mining Engineering Mining &
Metallurgical Engineering Dept, Faculty of Engineering, Assiut University. 157 P.
107
References
W. M. Telford et al, 1974 "Applied Geophysics", Cambridge University. 860 P.
Abo El-Hagag E. El-Sabry et al, 1990 “Gold Mineralization of The Hangaliy Area at
Eastern Desert”, Mining & Metallurgical Engineering Department, Faculty of
Engineering, Assiut University. 61 P.
Eugene P. Pfleider et al, 1968 "Surface Mining", The American Institute of Mining,
Metallurgical, and Petroleum Engineers, Inc. New York. 1048 P.
"Phosphate Rock and its Characteristics" The Article Originally Appeared in the
Journal Phosphorus & Potassium, Issue No: 217, (September-October, 1998), Electronic
Version on: http://www.nhm.ac.uk/mineralogy/phos/p&k217/steen.htm.
Ahmed, S. S. (2001). “Three-dimensional Characterisation of Groundwater
Parameters around Mines and Landfill Sites”. PH.D., Thesis, Royal School of
Mines, Imperial College of Science, Technology & Medicine, London, UK.
Issak, E. H. and Srivastava, R. M. (1989). “An Introduction to Applied Geostatistics”.
Oxford Univ. Press, New York, 561 p.
Nakhla, F. M. (1990). “Geology and Characteristics of Developed Main Phosphate
Seam in Mahamied Phosphatefield, North Sinai, Egypt”. Proceedings of 7th
Symposium, Phaner. Develop. Egypt. PP. 65-92.
Rashad, M. Z. (1999). A Brief Course in Application of Computer Methods in Mining
Industry. A course for 2nd year mining. Mining & Met. Eng. Dept., Faculty of
Engineering, Assiut University, Egypt.
Rashad, M. Z. (2003). “Principles of Mining Geostatistics”. Lecture Notes, 4th Year
Mining Engineering, Mining and Metallurgical Engineering Department, Assuit
University.
Weller, J. M. (1960). “Stratigraphic Principles & Practice”.
Web Sites:
http://www.uk-rocks.net.
http://www.elnasrmining.com.
http://Sanangelo.Tamu.Edu/Agronomy/Mg/Phospht.htm.
www.softwallequipment.com
Software’s:
Microsoft Office 2000 (Word, Excel and Power Point), (2000).
ORACLE® Database. Release 9.0.0, ORACLE Corp, (2001).
SGWIN, Statistical Graphics under Windows, (1998).
SURFUR 7. Release 7.0, Golden® Software, Inc., (1993-1999).
VARIOWIN, Release 2.21, Yvan Pannatier el al, (1993-1998).
108
Appendix
I.1
I
Original Data
X, Y Coordinates,"t"and P2O5 of Sampling Points at Mahamid
Table I-1 summarizes the original data of area I at El Mahamid district. X, Y,"t"
and P2O5 of the ore deposit at the different borehole locations are given in
meters
Table I-1: Co-ordinates of old drilled boreholes at Mahamid phosphate mine, Esna.
B.H No.
X (m)
Y (m)
K-15
K-16
K-17
K-18
K-19
K-20
K-21
K-22
K-23
K-24
L-13
801515
801980
802290
802743
803110
803610
803819
804290
804549
805153
800651
277460
277430
277423
277590
277460
277480
277495
277517
277460
277107
277790
t (m) P2O5%
0.25
0.35
0.25
0.40
0.15
1.00
1.40
0.75
0.40
0.30
0.35
21.56
21.75
21.10
20.83
10.67
29.47
28.59
25.29
25.66
26.66
8.19
Appendix II
Other Results of Data Analysis
Table I-1: Cont.
B.H No.
X (m)
Y (m)
L-14
L-15
L-16
L-17
L-19
L-20
L-21
L-22
L-23
L-25
M-13
M-14
M-15
M-16
M-17
M-18
M-19
M-20
M-21
M-23
M-24
M-25
N-13
N-14
N-15
N-16
N-17
N-18
N-19
N-20
N-21
N-22
N-23
N-25
O-14
O-15
O-16
O-17
O-18
O-19
O-20
O-21
O-22
O-23
O-26
P-17
P-18
P-21
P-25
Q-21
R-18
801160
801526
801858
802297
803020
803560
803805
804275
804748
805338
800709
801115
801519
801876
802320
802665
803010
803805
803805
804667
805025
805341
800782
801128
801501
801558
802258
802657
803013
803475
803820
804238
804657
804506
801027
801489
801889
802243
802668
802992
803401
803870
804225
804568
805783
802240
802649
803775
805410
803750
802647
277810
277820
277845
277757
277860
277882
277873
277858
277920
277902
278190
278163
278218
278205
278220
278218
278225
278250
278252
278250
278252
278315
278609
278570
278540
278588
278602
278621
278627
278650
278655
278641
278716
278702
278935
278870
279040
279010
278960
279036
279030
279060
279071
279048
279071
279337
279337
279463
279451
279801
280090
t (m) P2O5%
0.50
1.20
0.8
0.25
0.92
1.20
0.50
0.70
0.65
0.40
0.35
0.45
1.50
0.90
0.70
0.50
0.90
1.00
0.90
0.65
0.40
0.20
0.30
0.95
0.60
0.95
0.65
0.80
0.90
0.75
0.60
0.55
0.80
0.80
0.40
1.4
0.25
0.30
0.80
1.55
1.40
0.80
0.65
0.75
0.30
0.70
1.25
0.45
0.30
0.75
1.00
18.50
24.55
25.45
19.47
25.90
26.87
26.58
24.57
24.13
18.86
16.32
22.39
23.41
29.09
25.66
19.23
25.66
25.65
25.45
22.75
15.82
15.17
19.40
25.45
22.54
24.38
23.77
23.93
25.66
19.04
27.07
20.93
25.45
24.69
27.00
13.65
23.38
18.12
22.16
21.37
27.94
25.98
26.78
27.49
10.93
25.35
17.33
25.25
20.45
24.21
25.05
110
Appendix II
Other Results of Data Analysis
Table I.1: Cont.
B.H No.
X (m)
Y (m)
I-22
J-15
J-16
J-17
J-20
J-21
J-22
J-23
804260
801525
801914
802240
803495
803565
804230
804480
276869
277073
277050
277020
277090
277115
277120
277115
t (m) P2O5%
0.60
0.85
0.50
0.20
0.90
0.65
0.60
0.65
23.14
29.84
24.90
21.80
21.61
28.16
29.61
28.16
111
Appendix II
Appendix
II.1
Other Results of Data Analysis
II
Other Results of Data Analysis
X, Y Coordinates,"t" and P2O5 of Sampling Points
Table II-1 summarizes the original data of area II at El Mahamid district. X, Y,"t"
and P2O5 of the ore deposit at the different borehole locations are given in
meters.
Table II-1: X Y, Co-ordinates, thickness and Assay at drilled boreholes at Mahamid phosphate mine.
B.H. No.
X (m)
Y (m)
t (m)
P2O5
A-17
A-19
A-20
A-25
A-26
A-27
A-28
B-17
B-19
B-20
B-21
B-22
802330
803150
803490
805410
805790
806200
806598
802380
803070
803475
803850
804250
273540
273537
273560
273548
273557
273548
273560
273927
273940
273927
273927
273957
0.25
0.80
0.50
1.05
0.35
0.30
0.40
0.20
0.20
1.15
0.55
0.60
21.09
22.10
22.26
20.83
16.80
16.43
20.55
20.74
19.49
22.27
24.69
24.73
112
Appendix II
Other Results of Data Analysis
Table II.1: Cont.
B.H. No.
X (m)
Y (m)
t (m)
P2O5%
B-24
B-25
B-26
B-27
B-28
C-17
C-19
C-20
C-21
C-22
C-23
C-24
C-25
C-26
C-27
C-28
D-17
D-18
D-19
D-20
D-21
D-22
D-23
D-24
D-25
D-26
D-27
D-28
D-29
E-21
E-22
E-23
E-25
E-26
E-27
E-28
E-29
E-30
F-17
F-18
F-19
F-20
F-21
F-22
F-23
F-24
F-25
F-26
F-27
F-28
F-29
F-30
804995
805410
805796
806215
806590
802330
803040
803420
803805
804230
804601
804990
805398
805780
806190
806570
802330
802630
803010
803400
803775
804192
804580
804970
805375
805760
806150
806450
806940
803770
804169
804550
805387
805720
806140
806540
806905
807320
802130
802590
802980
803350
803740
804150
804550
804930
805325
805710
806110
806501
806901
807280
273975
273957
273950
273935
273950
274330
274338
274330
274329
274329
274330
274352
274352
274352
274352
274348
274719
274720
274728
274724
274723
274730
274756
274740
274740
274735
274723
274728
274756
275130
275145
275145
275151
275163
275150
275153
275175
275090
275527
275550
275557
275560
275555
275557
275555
275560
275560
275560
275550
275560
275570
275598
0.60
0.50
0.35
0.3
0.45
0.30
0.90
1.50
1.3
0.45
0.60
0.55
0.60
0.50
0.30
0.20
0.20
0.50
0.55
0.65
0.95
1.05
0.6
1.4
0.45
0.4
0.80
0.50
1.25
0.5
0.45
0.85
0.65
0.35
0.40
0.80
0.55
0.35
0.70
0.30
1.30
0.75
0.60
0.80
1.00
0.67
0.78
0.40
0.30
0.55
0.45
0.45
24.11
21.87
17.77
17.99
23.85
24.96
23.08
24.58
23.36
21.82
16.66
22.68
23.08
27.58
27.31
22.12
25.72
26.54
18.75
27.53
28.75
18.17
17.86
24.98
23.24
23.72
21.09
27.71
20.80
24.81
26.58
23.70
23.91
25.78
23.55
22.87
17.09
11.28
27.55
20.54
26.52
30.35
24.81
28.36
25.12
20.79
23.82
25.04
17.91
20.14
17.16
12.89
113
Appendix II
Other Results of Data Analysis
Table II.1: Cont.
B.H. No.
X (m)
Y (m)
t (m)
P2O5%
G-17
G-18
G-19
G-20
G-21
G-22
G-23
G-24
G-25
G-26
G-27
G-28
G-29
G-30
G-31
G-32
G-33
H-17
H-19
H-20
H-24
H-25
H-26
H-27
H-28
H-29
H-30
H-31
H-32
H-33
H-34
I-25
I-26
I-28
I-29
I-30
I-31
I-32
I-33
I-34
I-35
J24
J25
J34
B'24
B'25
B'26
B'27
B'28
C'23
C'24
C'25
802192
802580
802980
803340
803710
804148
804565
804905
805320
805700
806098
806498
806890
807270
807660
808145
808479
802190
802910
803330
805160
805301
805670
806075
806460
806860
807250
807640
808125
808520
808909
805260
805630
806440
806850
807237
807630
808101
808515
808827
809251
805130
805301
808870
805010
805410
805796
806190
806610
804660
805040
805450
275900
275920
275930
275933
275945
275908
275803
275950
275945
275940
275940
275950
275970
275990
276020
2760580
276085
276170
276348
276190
276360
276353
276353
276250
276360
276390
276437
276456
276475
276510
276540
276775
276691
276676
276790
276828
276840
276859
276890
276965
276885
277115
276960
277110
273180
273160
273150
273201
273290
272755
272740
272755
1.40
0.15
0.60
0.45
1.10
0.95
1.65
0.70
0.40
0.45
0.35
0.45
0.35
0.65
0.65
0.40
0.25
2.05
0.70
0.25
0.50
0.45
0.45
0.55
0.55
0.55
0.65
0.65
0.55
0.35
0.45
0.45
0.60
0.60
0.40
0.65
0.60
0.95
0.90
0.45
0.35
0.35
0.35
0.55
0.25
0.60
0.30
0.10
0.35
0.20
0.75
0.60
29.21.
30.32
24.81
31.10
27.61
25.62
23.98
29.91
24.39
19.65
21.18
15.85
15.73
20.79
16.26
24.37
21.81
25.62
18.35
20.41
23.13
21.80
18.35
20.81
16.00
22.13
15.48
18.17
25.95
30.20
25.63
28.25
23.97
19.64
30.06
21.24
25.25
25.32
28.74
27.70
25.35
23.02
29.35
27.48
16.34
.21.55
25.21
23.12
21.46
24.3
19.01
21.62
114
Appendix II
Other Results of Data Analysis
Table II.1: Cont.
B.H. No.
X (m)
Y (m)
t (m)
P2O5%
D'23
D'24
D'25
804880
805080
805468
272530
272348
272370
0.30
0.50
0.40
15.43
24.19
22.57
115
Appendix III
Appendix
Results of Area II
III
Results of Area II
III.1 Calculated tonnage and average assay at area II
As it has been mentioned before the study area II was divided into 5 zones,
named, (d,e,f,g, and h). Calculation of the average thickness, average assay and
total tonnage at each zone has been carried out using the same steps explained
in Chapter 4. Figures (III.1 through III.5) show the distribution of the boreholes
at each of the 5 zones respectively, while Figure (III.6) shows the over all area II.
116
Appendix III
Results of Area II
276600
276400
276200
276000
1
16
275800
X, m
2
1
15
275400
18
275200
20
19
5
6
12
11
7
13
14
17
275600
4
3
9
10
22
8
25
21
23
26
24
3
27
3
34
275000
35
274800
32
31
36
29
33
37
28
30
3
3
274600
802000
802500
803000
803500
804000
804500
Y, m
Figure III.1:
Triangulation net of zone "d" at El Mahamid area II.
275000
274000
X, m
3
7
4 5 6
8
23 223 21 20
18
19
17
3
3
3
3
3
3
27 28
25
29
26
39
24
40
38
3
41
43
44
42
47
3
45 46
48
49
1
274500
273500
273000
272500
272000
804000
2
804500
805000
805500
9
10
3
11
3
16
15
3
30
31
12
3
3
14
3
13
32
33
35
37 36
34
806000
806500
807000
Y, m
Figure III.2:
Triangulation net of zone "e" at El Mahamid area II.
117
Appendix III
Results of Area II
277500
277000
1
276500
X, m
276000
275500
275000
274500
7 9 10 16
3
5
6 11 12 13
4
31
35
33
29
34
32
28
36 37 38 39
43
42 41
40
44
2
8
25 24 26
23 22 27
15 17 18
21
19
14
20
30
45
274000
273500
806000
806500
Figure III.3:
807000
807500
Y, m
808000
808500
809000
809500
Triangulation net of zone "f" at El Mahamid area II.
277500
6
277000
X, m
276500
276000
30
30
31
30
275500
51
275000
274500
804000
5 7
56
55
8
4
9 13
54
3 10
12
2
11
53
1
28 27 26 25 24 23 22
34 37
39
33
38
32
35
36
48
46
47
52 50
49
804500
805000
805500
14
15
21
40
45
17
16
20
41
18
19
42
44
806000
43
806500
807000
Y, m
Figure III.4:
Triangulation net of zone "g" at El Mahamid area II.
118
Appendix III
Results of Area II
274800
274600
3
10
9
5
1
4
X, m
274400
274200
7
14
2
6
13
16
19
17
20
11
274000
273800
21
12
15
8
22
23
18
273600
273400
802000
802500
803000
803500
804000
804500
Y, m
Figure III.5:
Triangulation net of zone "h" at El Mahamid area II.
278000
277000
X,m
276000
275000
274000
273000
272000
801000 802000 803000 804000 805000 806000 807000 808000 809000 810000
Y, m
Figure III.6:
Triangulation net of area II at Eastern El Mahamid.
119
Appendix III
Results of Area II
Table III.1: Summary of Zone II of, El Mahamid area.
Zone
1
2
3
4
5
No.of Tri.
37
49
45
56
23
No.of B.H.
27
36
32
38
21
Area, m2
2784153
4261362
3785742
4504577
2061931
17397765
Av. Thick
0.733
0.495
0.551
0.624
0.700
Av. P2O5
25.56
21.7
20.82
23.37
23.28
Tonnage
3715573
3836305
3799033
5115320
2626814
19093045
Result of part II
No. of triangles
No. of B.H.
Area
Volume
Av.Thick.
Av.Assay
Tonnage
210
123
17323592
10444529.965
0.603
22.946
19009044.536
120